​​The ESolver is an iOS application that can generate an explicit solution of a linear system that has less than six equations. The solution is presented in a multilevel folded pattern that allows users to have a better understanding of an operation.


The style of the solution includes self-explanatory directive steps where a step may contain one or more steps. And this process may be repeated until a certain elementary algebraic operation (e.g. addition, subtraction, etc.) is reached.The current version of the ESolver, also provides a feature to generate sample systems using the Generate button, which is a great way to learn how to enter equations to the Workspace. The Validate button is the key to turn on the Solution navigation button. If validation fails, the Solution button will not be activated. To get a successful validation message, users need to follow all the rules that apply to entering the equations.


There are four different solvers that are available for you, which are:


  • Substitution of Variables: this allows you to solve a linear system using substitution of variable technique.
  • ​Elimination of Variables-Addition: this allows you to solve a linear system by successive elimination of variables. The elimination is done via adding two equations.
  • Elimination of Variables-Subtraction: this allows you to solve a linear system by successive elimination of variables. The elimination is done via subtraction. 
  • Just give me the solution: this provides you with just the answer of a solvable linear system.


This is a great app that can be used by students as a self-learning tool and by instructors for illustration purposes. We do not guarantee that it is completely bug free. So, you should not use the solution in any way that may put any of your valuables at risk. But we are working every day to make this app better.  


To obtain the solution an internet connection is not required. 

ESolver At A Glance

Sample Solution:


Numbering the entered equations:
X1 +X2 +4X3 -12X4 -2X5 = 17   ... 1 
X1 +72X2 +X3 +2X4 -2X5 = -3   ... 2+ Show More
Simplifying,
⇒ X1 + 32X2 - X3 + 2X2 + 2X4 - 2X5 = - 3 - 4X3 + 2X3
⇒ X1 + 72X2 - X3 + 2X4 - 2X5 = - 3 - 2X3+ Show More
L.H.S.
X1 + 32X2 - X3 + 2X2 + 2X4 - 2X5
X1 + 72X2 - X3 + 2X4 - 2X5+ Show More
32X2 + 2X2
[32 + 2]X2
72X2 + Show More
32 + 2
3×1 + 2×22
3+42
72

R.H.S.
= - 3 - 4X3 + 2X3
= - 3 - 2X3+ Show More
(-4)X3 + 2X3
[(-4) + 2]X3
= -2X3 + Show More
-4 + 2
= -2

Subtracting same quantity from both sides of the above equation,
⇒ [X1 + 72X2 - X3 + 2X4 - 2X5] - [- 2X3] = [- 3 - 2X3] - [- 2X3]
⇒ X1 + 72X2 + X3 + 2X4 - 2X5 = - 3+ Show More
L.H.S.
X1 + 72X2 - X3 + 2X4 - 2X5 + 2X3
X1 + 72X2 + X3 + 2X4 - 2X5+ Show More
(-1)X3 + 2X3
[(-1) + 2]X3
= 1X3 + Show More
-1 + 2
= 1

R.H.S.
= - 3 - 2X3 + 2X3
= - 3 + 0+ Show More
(-2)X3 + 2X3
[(-2) + 2]X3
= 0X3 + Show More
-2 + 2
= 0
52X1 +32X2 +3X3     = 854   ... 3 
2X1 -32X2 +3X3     = 252   ... 4 
5X1 -X2 +2X3     = 2   ... 5 

Reorganizing the system:
52X1 +32X2 +3X3     = 854   ... 6 Same as 3
2X1 -32X2 +3X3     = 252   ... 7 Same as 4
5X1 -X2 +2X3     = 2   ... 8 Same as 5
X1 +72X2 +X3 +2X4 -2X5 = -3   ... 9 Same as 2
X1 +X2 +4X3 -12X4 -2X5 = 17   ... 10 Same as 1

Eliminating variable X1 from equation 6 and 7
274X2 + 32X3 = - 454   ... 11+ Show More
We have,
52X1 +32X2 +3X3 = 854
2X1 -32X2 +3X3 = 252


Multiplying the first and second equations by -2 and 52 respectively we get,

-5X1 -3X2 -6X3 = -852+ Show More
L.H.S.
[52X1 + 32X2 + 3X3]×-2
[52X1×-2] + [32X2×-2] + [3X3×-2]
= - 5X1 - 3X2 - 6X3 + Show More
Simplification 1:
52X1×(-2)
[52×(-2)]X1
= -5X1 + Show More
52×(-2)
51×2×-1×21
52×-1×21
51×-11
= -5

Simplification 2:
32X2×(-2)
[32×(-2)]X2
= -3X2 + Show More
32×(-2)
31×2×-1×21
32×-1×21
31×-11
= -3

Simplification 3:
3X3×(-2)
[3×(-2)]X3
= -6X3 + Show More
3×(-2)
= -6



R.H.S.
[854]×-2
[854×-2]
= - 852 + Show More
854×(-2)
-852 + Show More
854×(-2)
852×2×-1×21
852×-1×21
852×-11
-852
5X1 -154X2 +152X3 = 1254+ Show More
L.H.S.
[2X1 - 32X2 + 3X3]×52
[2X1×52] + [-32X2×52] + [3X3×52]
= 5X1 - 154X2 + 152X3 + Show More
Simplification 1:
2X1×52
[52]X1
= 5X1 + Show More
52
1×21×51×2
21×52
11×51
= 5

Simplification 2:
-32X2×52
[-32×52]X2
-154X2 + Show More
-32×52
(-3)×52×2
-154

Simplification 3:
3X3×52
[52]X3
152X3 + Show More
52
3×51×2
152



R.H.S.
[252]×52
[252×52]
1254 + Show More
252×52
1254 + Show More
252×52
25×52×2
1254


Adding these two equations we get,

 -5X1 -3X2 -6X3 = -852 
(+)5X1 -154X2 +152X3 = 1254 
   -274X2 +32X3 = -454+ Show More
L.H.S.
[- 5X1 - 3X2 - 6X3] + [5X1 - 154X2 + 152X3]
= - 5X1 - 3X2 - 6X3 + 5X1 - 154X2 + 152X3
= - 5X1 + 5X1 - 3X2 - 154X2 - 6X3 + 152X3
= 0 - 274X2 + 32X3+ Show More
Simplification 1:
(-5)X1 + 5X1
[(-5) + 5]X1
= 0X1 + Show More
-5 + 5
= 0

Simplification 2:
(-3)X2 + -154X2
[(-3) + -154]X2
-274X2 + Show More
-3 + -154
(-3)×4 + (-15)×14
(-12)+(-15)4
-274

Simplification 3:
(-6)X3 + 152X3
[(-6) + 152]X3
32X3 + Show More
-6 + 152
(-6)×2 + 15×12
(-12)+152
32


= - 274X2 + 32X3

R.H.S.
[852] + [1254]
= - 852 + 1254
= - 454+ Show More
-852 + 1254
-454 + Show More
-852 + 1254
(-85)×4 + 125×22×4
(-340)+2508
-908
-454×22
-454×1
-454
Eliminating variable X1 from equation 7 and 8
112X2 - 11X3 = - 1172   ... 12+ Show More
We have,
2X1 -32X2 +3X3 = 252
5X1 -X2 +2X3 = 2


Multiplying the first and second equations by -5 and 2 respectively we get,

-10X1 +152X2 -15X3 = -1252+ Show More
L.H.S.
[2X1 - 32X2 + 3X3]×-5
[2X1×-5] + [-32X2×-5] + [3X3×-5]
= - 10X1 + 152X2 - 15X3 + Show More
Simplification 1:
2X1×(-5)
[2×(-5)]X1
= -10X1 + Show More
2×(-5)
= -10

Simplification 2:
-32X2×(-5)
[-32×(-5)]X2
152X2 + Show More
-32×(-5)
(-3)×(-5)2×1
152

Simplification 3:
3X3×(-5)
[3×(-5)]X3
= -15X3 + Show More
3×(-5)
= -15



R.H.S.
[252]×-5
[252×-5]
= - 1252 + Show More
252×(-5)
-1252 + Show More
252×(-5)
25×(-5)2×1
-1252
10X1 -2X2 +4X3 = 4+ Show More
L.H.S.
[5X1 - X2 + 2X3]×2
[5X1×2] + [-X2×2] + [2X3×2]
= 10X1 - 2X2 + 4X3 + Show More
Simplification 1:
5X1×2
[5×2]X1
= 10X1 + Show More
5×2
= 10

Simplification 2:
(-1)X2×2
[(-1)×2]X2
= -2X2 + Show More
(-1)×2
= -2

Simplification 3:
2X3×2
[2×2]X3
= 4X3 + Show More
2×2
= 4



R.H.S.
[2]×2
[2×2]
= 4 + Show More
2×2
= 4 + Show More
2×2
= 4


Adding these two equations we get,

 -10X1 +152X2 -15X3 = -1252 
(+)10X1 -2X2 +4X3 = 4 
   +112X2 -11X3 = -1172+ Show More
L.H.S.
[- 10X1 + 152X2 - 15X3] + [10X1 - 2X2 + 4X3]
= - 10X1 + 152X2 - 15X3 + 10X1 - 2X2 + 4X3
= - 10X1 + 10X1 + 152X2 - 2X2 - 15X3 + 4X3
= 0 + 112X2 - 11X3+ Show More
Simplification 1:
(-10)X1 + 10X1
[(-10) + 10]X1
= 0X1 + Show More
-10 + 10
= 0

Simplification 2:
152X2 + (-2)X2
[152 + (-2)]X2
112X2 + Show More
152 + -2
15×1 + (-2)×22
15+(-4)2
112

Simplification 3:
(-15)X3 + 4X3
[(-15) + 4]X3
= -11X3 + Show More
-15 + 4
= -11


112X2 - 11X3

R.H.S.
[1252] + [4]
= - 1252 + 4
= - 1172+ Show More
-1252 + 4
-1172 + Show More
-1252 + 4
(-125)×1 + 4×22
(-125)+82
-1172

Eliminating variable X2 from equation 11 and 12
66X3 = 18274   ... 13+ Show More
We have,
-274X2 +32X3 = -454
112X2 -11X3 = -1172


Multiplying the first and second equations by -112 and -274 respectively we get,

2978X2 -334X3 = 4958+ Show More
L.H.S.
[274X2 + 32X3]×-112
[-274X2×-112] + [32X3×-112]
2978X2 - 334X3 + Show More
Simplification 1:
-274X2×-112
[-274×-112]X2
2978X2 + Show More
-274×-112
(-27)×(-11)4×2
2978

Simplification 2:
32X3×-112
[32×-112]X3
-334X3 + Show More
32×-112
3×(-11)2×2
-334



R.H.S.
[454]×-112
[-454×-112]
4958 + Show More
-454×-112
4958 + Show More
-454×-112
(-45)×(-11)4×2
4958
-2978X2 +2974X3 = 31598+ Show More
L.H.S.
[112X2 - 11X3]×-274
[112X2×-274] + [-11X3×-274]
= - 2978X2 + 2974X3 + Show More
Simplification 1:
112X2×-274
[112×-274]X2
-2978X2 + Show More
112×-274
11×(-27)2×4
-2978

Simplification 2:
(-11)X3×-274
[(-11)×-274]X3
2974X3 + Show More
(-11)×-274
(-11)×(-27)1×4
2974



R.H.S.
[1172]×-274
[-1172×-274]
31598 + Show More
-1172×-274
31598 + Show More
-1172×-274
(-117)×(-27)2×4
31598


Adding these two equations we get,

 2978X2 -334X3 = 4958 
(+)-2978X2 +2974X3 = 31598 
   +66X3 = 18274+ Show More
L.H.S.
[2978X2 - 334X3] + [2978X2 + 2974X3]
2978X2 - 334X3 - 2978X2 + 2974X3
2978X2 - 2978X2 - 334X3 + 2974X3
= 0 + 66X3+ Show More
Simplification 1:
2978X2 + -2978X2
[2978 + -2978]X2
= 0X2 + Show More
2978 + -2978
297 + (-297)8
08
= 0

Simplification 2:
-334X3 + 2974X3
[-334 + 2974]X3
= 66X3 + Show More
-334 + 2974
(-33) + 2974
2644
= 66×44
= 66×1
= 66


= 66X3

R.H.S.
[4958] + [31598]
4958 + 31598
18274+ Show More
4958 + 31598
18274 + Show More
4958 + 31598
495 + 31598
36548
18274×22
18274×1
18274

Solving equation 13 for variable X3 we get,
X3 = 60988  Ans.    ... 14+ Show More
66X3 = 18274
Dividing both sides of the above equation by same number,
⇒ [66X3] ÷ [66] = [18274] ÷ [66]
⇒ X3 = 60988+ Show More
L.H.S.
[66X3]÷66
[66X3÷66]
X3 + Show More
66X3÷66
[66÷66]X3
= 1X3 + Show More
66 ÷ 66
= 66×166
1×661×11×66
661×166
11×11
= 1


R.H.S.
[18274]÷66
[18274÷66]
60988 + Show More
18274÷66
60988 + Show More
18274 ÷ 66
18274×166
609×34×122×3
609×34×122×3
6094×122
60988
Substituting the value of variable X3 from equation 14 into 11 we get,
X2 = 14144  Ans.    ... 15+ Show More
Substituting the following equation,
X3 = 60988
into
274X2 + 32X3 = - 454
we have,
⇒  - 274X2 + 32×[60988] =  - 454
⇒ - 274X2 + 1827176 = - 454+ Show More
L.H.S.
=  - 274X2 + 32×[60988]
= - 274X2 + [32×60988]
= - 274X2 + 1827176+ Show More
60988×32
1827176 + Show More
60988×32
609×388×2
1827176


R.H.S.
=  - 454

Subtracting same quantity from both sides of the above equation,
⇒ [274X2 + 1827176] - [1827176] = [454] - [1827176]
⇒ - 274X2 = - 3807176+ Show More
L.H.S.
= - 274X2 + 1827176 - 1827176
= - 274X2 + 0+ Show More
1827176 + -1827176
= 0 + Show More
1827176 + -1827176
1827 + (-1827)176
0176
= 0

R.H.S.
= - 454 - 1827176
= - 3807176+ Show More
-454 + -1827176
-3807176 + Show More
-454 + -1827176
(-45)×176 + (-1827)×44×176
(-7920)+(-7308)704
-15228704
-3807176×44
-3807176×1
-3807176

Dividing both sides of the above equation by same number,
⇒ [274X2] ÷ [274] = [3807176] ÷ [274]
⇒ X2 = 14144+ Show More
L.H.S.
[274X2]÷-274
[-274X2÷-274]
X2 + Show More
-274X2÷-274
[-274÷-274]X2
= 1X2 + Show More
-274 ÷ -274
-274×4-27
1×-271×4×1×41×-27
-274×4-27
11×11
= 1


R.H.S.
[3807176]÷-274
[-3807176÷-274]
14144 + Show More
-3807176÷-274
14144 + Show More
-3807176 ÷ -274
-3807176×4-27
141×-2744×4×1×41×-27
141×-2744×4×4-27
14144×11
14144
Substituting the value of variables X3 and X2 from equations 14 and 15 into 6 we get,
X1 = - 1911  Ans.    ... 16+ Show More
Substituting the following equations,
X3 = 60988
X2 = 14144
into
52X1 + 32X2 + 3X3 = 854
we have,
⇒ 52X1 + 32×[14144] + 3×[60988] = 854
⇒ 52X1 + 112544 = 854+ Show More
L.H.S.
52X1 + 32×[14144] + 3×[60988]
52X1 + [32×14144] + [60988]
52X1 + 42388 + 182788+ Show More
Simplification 1:
14144×32
42388 + Show More
14144×32
141×344×2
42388

Simplification 2:
60988×3
182788 + Show More
14144×32
141×344×2
42388


52X1 + 112544+ Show More
42388 + 182788
112544 + Show More
42388 + 182788
423 + 182788
225088
112544×22
112544×1
112544


R.H.S.
854

Subtracting same quantity from both sides of the above equation,
⇒ [52X1 + 112544] - [112544] = [854] - [112544]
⇒ 52X1 = - 9522+ Show More
L.H.S.
52X1 + 112544 - 112544
52X1 + 0+ Show More
112544 + -112544
= 0 + Show More
112544 + -112544
1125 + (-1125)44
044
= 0

R.H.S.
854 - 112544
= - 9522+ Show More
854 + -112544
-9522 + Show More
854 + -112544
85×44 + (-1125)×44×44
3740+(-4500)176
-760176
-9522×88
-9522×1
-9522

Dividing both sides of the above equation by same number,
⇒ [52X1] ÷ [52] = [9522] ÷ [52]
⇒ X1 = - 1911+ Show More
L.H.S.
[52X1]÷52
[52X1÷52]
X1 + Show More
52X1÷52
[52÷52]X1
= 1X1 + Show More
52 ÷ 52
52×25
1×51×2×1×21×5
52×25
11×11
= 1


R.H.S.
[9522]÷52
[-9522÷52]
= - 1911 + Show More
-9522÷52
-1911 + Show More
-9522 ÷ 52
-9522×25
-19×511×2×1×21×5
-19×511×2×25
-1911×11
-1911

Substituting the value of variables X3, X2 and X1 from equations 14, 15 and 16 into 9 and 10 we get,
-2X4 +2X5 = 42722   ... 17+ Show More
Substituting the following equations,
X3 = 60988
X2 = 14144
X1 = - 1911
into
X1 + 72X2 + X3 + 2X4 - 2X5 = - 3
we have,
⇒ 1×[1911] + 72×[14144] + 1×[60988] + 2X4 - 2X5 =  - 3
⇒ 144488 + 2X4 - 2X5 = - 3+ Show More
L.H.S.
= 1×[1911] + 72×[14144] + 1×[60988] + 2X4 - 2X5
[-1911] + [72×14144] + [60988] + 2X4 - 2X5
= - 1911 + 98788 + 60988 + 2X4 - 2X5+ Show More
Simplification 1:
-1911×1
-1911 + Show More
-1911×1
(-19)×111×1
-1911

Simplification 2:
14144×72
98788 + Show More
-1911×1
(-19)×111×1
-1911

Simplification 3:
60988×1
60988 + Show More
-1911×1
(-19)×111×1
-1911


144488 + 2X4 - 2X5+ Show More
-1911+98788+60988
144488 + Show More
-1911 + 98788 + 60988
(-19)×8 + 987×1 + 609×188
(-152)+987+60988
144488
36122×44
36122×1
36122


R.H.S.
=  - 3

Subtracting same quantity from both sides of the above equation,
⇒ [144488 + 2X4 - 2X5] - [144488] = [- 3] - [144488]
⇒ 2X4 - 2X5 = - 42722+ Show More
L.H.S.
144488 + 2X4 - 2X5 - 144488
= 0 + 2X4 - 2X5+ Show More
144488 + -144488
= 0 + Show More
144488 + -144488
1444 + (-1444)88
088
= 0

R.H.S.
= - 3 - 144488
= - 42722+ Show More
(-3) + -144488
-42722 + Show More
-3 + -144488
(-3)×88 + (-1444)×188
(-264)+(-1444)88
-170888
-42722×44
-42722×1
-42722

Dividing both sides of the above equation by same number,
⇒ [2X4 - 2X5] ÷ [- 1] = [42722] ÷ [- 1]
⇒ - 2X4 + 2X5 = 42722+ Show More
L.H.S.
[2X4 - 2X5]÷-1
[2X4÷-1] + [-2X5÷-1]
= - 2X4 + 2X5 + Show More
Simplification 1:
2X4÷(-1)
[2÷(-1)]X4
= -2X4 + Show More
2 ÷ (-1)
= 2×1-1
= -2×-1-1
= -2×1
= -2

Simplification 2:
(-2)X5÷(-1)
[(-2)÷(-1)]X5
= 2X5 + Show More
(-2) ÷ (-1)
= (-2)×1-1
= 2×-1-1
= 2×1
= 2



R.H.S.
[42722]÷-1
[-42722÷-1]
42722 + Show More
-42722÷(-1)
42722 + Show More
-42722 ÷ (-1)
-42722×1-1
42722×-1-1
42722×1
42722
12X4 +2X5 = 53544   ... 18+ Show More
Substituting the following equations,
X3 = 60988
X2 = 14144
X1 = - 1911
into
X1 + X2 + 4X3 - 12X4 - 2X5 = 17
we have,
⇒ 1×[1911] + 1×[14144] + 4×[60988] - 12X4 - 2X5 = 17
⇒ 128344 - 12X4 - 2X5 = 17+ Show More
L.H.S.
= 1×[1911] + 1×[14144] + 4×[60988] - 12X4 - 2X5
[-1911] + [14144] + [60988] - 12X4 - 2X5
= - 1911 + 14144 + 60922 - 12X4 - 2X5+ Show More
Simplification 1:
-1911×1
-1911 + Show More
-1911×1
(-19)×111×1
-1911

Simplification 2:
14144×1
14144 + Show More
-1911×1
(-19)×111×1
-1911

Simplification 3:
60988×4
60922 + Show More
-1911×1
(-19)×111×1
-1911


128344 - 12X4 - 2X5+ Show More
-1911+14144+60922
128344 + Show More
-1911 + 14144 + 60922
(-19)×4 + 141×1 + 609×244
(-76)+141+121844
128344


R.H.S.
= 17

Subtracting same quantity from both sides of the above equation,
⇒ [128344 - 12X4 - 2X5] - [128344] = [17] - [128344]
⇒ - 12X4 - 2X5 = - 53544+ Show More
L.H.S.
128344 - 12X4 - 2X5 - 128344
= 0 - 12X4 - 2X5+ Show More
128344 + -128344
= 0 + Show More
128344 + -128344
1283 + (-1283)44
044
= 0

R.H.S.
= 17 - 128344
= - 53544+ Show More
17 + -128344
-53544 + Show More
17 + -128344
17×44 + (-1283)×144
748+(-1283)44
-53544

Dividing both sides of the above equation by same number,
⇒ [12X4 - 2X5] ÷ [- 1] = [53544] ÷ [- 1]
⇒ 12X4 + 2X5 = 53544+ Show More
L.H.S.
[12X4 - 2X5]÷-1
[-12X4÷-1] + [-2X5÷-1]
12X4 + 2X5 + Show More
Simplification 1:
-12X4÷(-1)
[-12÷(-1)]X4
12X4 + Show More
-12 ÷ (-1)
-12×1-1
12×-1-1
12×1
12

Simplification 2:
(-2)X5÷(-1)
[(-2)÷(-1)]X5
= 2X5 + Show More
(-2) ÷ (-1)
= (-2)×1-1
= 2×-1-1
= 2×1
= 2



R.H.S.
[53544]÷-1
[-53544÷-1]
53544 + Show More
-53544÷(-1)
53544 + Show More
-53544 ÷ (-1)
-53544×1-1
53544×-1-1
53544×1
53544

Eliminating variable X4 from equation 17 and 18
10X5 = 149722   ... 19+ Show More
We have,
-2X4 +2X5 = 42722
12X4 +2X5 = 53544


Multiplying the second equation by 4 we get,

-2X4 +2X5 = 42722 
2X4 +8X5 = 53511+ Show More
L.H.S.
[12X4 + 2X5]×4
[12X4×4] + [2X5×4]
= 2X4 + 8X5 + Show More
Simplification 1:
12X4×4
[12×4]X4
= 2X4 + Show More
12×4
11×2×2×21
12×21
11×21
= 2

Simplification 2:
2X5×4
[2×4]X5
= 8X5 + Show More
2×4
= 8



R.H.S.
[53544]×4
[53544×4]
53511 + Show More
53544×4
53511 + Show More
53544×4
53511×4×1×41
53511×4×41
53511×11
53511


Adding these two equations we get,

 -2X4 +2X5 = 42722 
(+)2X4 +8X5 = 53511 
   +10X5 = 149722+ Show More
L.H.S.
[- 2X4 + 2X5] + [2X4 + 8X5]
= - 2X4 + 2X5 + 2X4 + 8X5
= - 2X4 + 2X4 + 2X5 + 8X5
= 0 + 10X5+ Show More
Simplification 1:
(-2)X4 + 2X4
[(-2) + 2]X4
= 0X4 + Show More
-2 + 2
= 0

Simplification 2:
2X5 + 8X5
[2 + 8]X5
= 10X5 + Show More
2 + 8
= 10


= 10X5

R.H.S.
[42722] + [53511]
42722 + 53511
149722+ Show More
42722 + 53511
149722 + Show More
42722 + 53511
427×11 + 535×2222×11
4697+11770242
16467242
149722×1111
149722×1
149722

Solving equation 19 for variable X5 we get,
X5 = 1497220  Ans.    ... 19+ Show More
10X5 = 149722
Dividing both sides of the above equation by same number,
⇒ [10X5] ÷ [10] = [149722] ÷ [10]
⇒ X5 = 1497220+ Show More
L.H.S.
[10X5]÷10
[10X5÷10]
X5 + Show More
10X5÷10
[10÷10]X5
= 1X5 + Show More
10 ÷ 10
= 10×110
1×101×11×10
101×110
11×11
= 1


R.H.S.
[149722]÷10
[149722÷10]
1497220 + Show More
149722÷10
1497220 + Show More
149722 ÷ 10
149722×110
1497220
Substituting the value of variable X5 from equation 19 into 17 we get,
X4 = - 2910  Ans.    ... 20+ Show More
Substituting the following equation,
X5 = 1497220
into
- 2X4 + 2X5 = 42722
we have,
⇒  - 2X4 + 2×[1497220] = 42722
⇒ - 2X4 + 1497110 = 42722+ Show More
L.H.S.
=  - 2X4 + 2×[1497220]
= - 2X4 + [1497220]
= - 2X4 + 1497110+ Show More
1497220×2
1497110 + Show More
1497220×2
1497110×2×1×21
1497110×2×21
1497110×11
1497110


R.H.S.
42722

Subtracting same quantity from both sides of the above equation,
⇒ [- 2X4 + 1497110] - [1497110] = [42722] - [1497110]
⇒ - 2X4 = 295+ Show More
L.H.S.
= - 2X4 + 1497110 - 1497110
= - 2X4 + 0+ Show More
1497110 + -1497110
= 0 + Show More
1497110 + -1497110
1497 + (-1497)110
0110
= 0

R.H.S.
42722 - 1497110
295+ Show More
42722 + -1497110
295 + Show More
42722 + -1497110
427×110 + (-1497)×2222×110
46970+(-32934)2420
140362420
295×484484
295×1
295

Dividing both sides of the above equation by same number,
⇒ [- 2X4] ÷ [- 2] = [295] ÷ [- 2]
⇒ X4 = - 2910+ Show More
L.H.S.
[- 2X4]÷-2
[-2X4÷-2]
X4 + Show More
(-2)X4÷(-2)
[(-2)÷(-2)]X4
= 1X4 + Show More
(-2) ÷ (-2)
= (-2)×1-2
1×-21×11×-2
-21×1-2
11×11
= 1


R.H.S.
[295]÷-2
[295÷-2]
= - 2910 + Show More
295÷(-2)
-2910 + Show More
295 ÷ (-2)
295×1-2
-2910×-1-1
-2910×1
-2910

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