​​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.

#### Sample Solution:

Numbering the entered equations:
 X1 + X2 + 4X3 - 12X4 - 2X5 = 17 ... 1 X1 + 72X2 + X3 + 2X4 - 2X5 = -3 ... 2 + Show MoreSimplifying,⇒ X1 + 32X2 - X3 + 2X2 + 2X4 - 2X5 = - 3 - 4X3 + 2X3⇒ X1 + 72X2 - X3 + 2X4 - 2X5 = - 3 - 2X3+ Show MoreL.H.S.= X1 + 32X2 - X3 + 2X2 + 2X4 - 2X5= X1 + 72X2 - X3 + 2X4 - 2X5+ Show More32X2 + 2X2= [32 + 2]X2= 72X2 + Show More32 + 2= 3×1 + 2×22= 3+42= 72R.H.S.= - 3 - 4X3 + 2X3= - 3 - 2X3+ Show More(-4)X3 + 2X3= [(-4) + 2]X3= -2X3 + Show More-4 + 2= -2Subtracting 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 MoreL.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= 1R.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 MoreL.H.S.= [52X1 + 32X2 + 3X3]×-2= [52X1×-2] + [32X2×-2] + [3X3×-2]= - 5X1 - 3X2 - 6X3 + Show MoreSimplification 1:52X1×(-2)= [52×(-2)]X1= -5X1 + Show More52×(-2)= 51×2×-1×21= 51×2×-1×21= 51×-11= -5Simplification 2:32X2×(-2)= [32×(-2)]X2= -3X2 + Show More32×(-2)= 31×2×-1×21= 31×2×-1×21= 31×-11= -3Simplification 3:3X3×(-2)= [3×(-2)]X3= -6X3 + Show More3×(-2)= -6R.H.S.= [854]×-2= [854×-2]= - 852 + Show More854×(-2)= -852 + Show More854×(-2)= 852×2×-1×21= 852×2×-1×21= 852×-11= -852 5X1 - 154X2 + 152X3 = 1254 + Show MoreL.H.S.= [2X1 - 32X2 + 3X3]×52= [2X1×52] + [-32X2×52] + [3X3×52]= 5X1 - 154X2 + 152X3 + Show MoreSimplification 1:2X1×52= [2×52]X1= 5X1 + Show More2×52= 1×21×51×2= 1×21×51×2= 11×51= 5Simplification 2:-32X2×52= [-32×52]X2= -154X2 + Show More-32×52= (-3)×52×2= -154Simplification 3:3X3×52= [3×52]X3= 152X3 + Show More3×52= 3×51×2= 152R.H.S.= [252]×52= [252×52]= 1254 + Show More252×52= 1254 + Show More252×52= 25×52×2= 1254

Adding these two equations we get,

 -5X1 - 3X2 - 6X3 = -852 (+) 5X1 - 154X2 + 152X3 = 1254 - 274X2 + 32X3 = -454 + Show MoreL.H.S.= [- 5X1 - 3X2 - 6X3] + [5X1 - 154X2 + 152X3]= - 5X1 - 3X2 - 6X3 + 5X1 - 154X2 + 152X3= - 5X1 + 5X1 - 3X2 - 154X2 - 6X3 + 152X3= 0 - 274X2 + 32X3+ Show MoreSimplification 1:(-5)X1 + 5X1= [(-5) + 5]X1= 0X1 + Show More-5 + 5= 0Simplification 2:(-3)X2 + -154X2= [(-3) + -154]X2= -274X2 + Show More-3 + -154= (-3)×4 + (-15)×14= (-12)+(-15)4= -274Simplification 3:(-6)X3 + 152X3= [(-6) + 152]X3= 32X3 + Show More-6 + 152= (-6)×2 + 15×12= (-12)+152= 32= - 274X2 + 32X3R.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 MoreL.H.S.= [2X1 - 32X2 + 3X3]×-5= [2X1×-5] + [-32X2×-5] + [3X3×-5]= - 10X1 + 152X2 - 15X3 + Show MoreSimplification 1:2X1×(-5)= [2×(-5)]X1= -10X1 + Show More2×(-5)= -10Simplification 2:-32X2×(-5)= [-32×(-5)]X2= 152X2 + Show More-32×(-5)= (-3)×(-5)2×1= 152Simplification 3:3X3×(-5)= [3×(-5)]X3= -15X3 + Show More3×(-5)= -15R.H.S.= [252]×-5= [252×-5]= - 1252 + Show More252×(-5)= -1252 + Show More252×(-5)= 25×(-5)2×1= -1252 10X1 - 2X2 + 4X3 = 4 + Show MoreL.H.S.= [5X1 - X2 + 2X3]×2= [5X1×2] + [-X2×2] + [2X3×2]= 10X1 - 2X2 + 4X3 + Show MoreSimplification 1:5X1×2= [5×2]X1= 10X1 + Show More5×2= 10Simplification 2:(-1)X2×2= [(-1)×2]X2= -2X2 + Show More(-1)×2= -2Simplification 3:2X3×2= [2×2]X3= 4X3 + Show More2×2= 4R.H.S.= [2]×2= [2×2]= 4 + Show More2×2= 4 + Show More2×2= 4

Adding these two equations we get,

 -10X1 + 152X2 - 15X3 = -1252 (+) 10X1 - 2X2 + 4X3 = 4 + 112X2 - 11X3 = -1172 + Show MoreL.H.S.= [- 10X1 + 152X2 - 15X3] + [10X1 - 2X2 + 4X3]= - 10X1 + 152X2 - 15X3 + 10X1 - 2X2 + 4X3= - 10X1 + 10X1 + 152X2 - 2X2 - 15X3 + 4X3= 0 + 112X2 - 11X3+ Show MoreSimplification 1:(-10)X1 + 10X1= [(-10) + 10]X1= 0X1 + Show More-10 + 10= 0Simplification 2:152X2 + (-2)X2= [152 + (-2)]X2= 112X2 + Show More152 + -2= 15×1 + (-2)×22= 15+(-4)2= 112Simplification 3:(-15)X3 + 4X3= [(-15) + 4]X3= -11X3 + Show More-15 + 4= -11= 112X2 - 11X3R.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 MoreL.H.S.= [- 274X2 + 32X3]×-112= [-274X2×-112] + [32X3×-112]= 2978X2 - 334X3 + Show MoreSimplification 1:-274X2×-112= [-274×-112]X2= 2978X2 + Show More-274×-112= (-27)×(-11)4×2= 2978Simplification 2:32X3×-112= [32×-112]X3= -334X3 + Show More32×-112= 3×(-11)2×2= -334R.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 MoreL.H.S.= [112X2 - 11X3]×-274= [112X2×-274] + [-11X3×-274]= - 2978X2 + 2974X3 + Show MoreSimplification 1:112X2×-274= [112×-274]X2= -2978X2 + Show More112×-274= 11×(-27)2×4= -2978Simplification 2:(-11)X3×-274= [(-11)×-274]X3= 2974X3 + Show More(-11)×-274= (-11)×(-27)1×4= 2974R.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 MoreL.H.S.= [2978X2 - 334X3] + [- 2978X2 + 2974X3]= 2978X2 - 334X3 - 2978X2 + 2974X3= 2978X2 - 2978X2 - 334X3 + 2974X3= 0 + 66X3+ Show MoreSimplification 1:2978X2 + -2978X2= [2978 + -2978]X2= 0X2 + Show More2978 + -2978= 297 + (-297)8= 08= 0Simplification 2:-334X3 + 2974X3= [-334 + 2974]X3= 66X3 + Show More-334 + 2974= (-33) + 2974= 2644= 66×44= 66×1= 66= 66X3R.H.S.= [4958] + [31598]= 4958 + 31598= 18274+ Show More4958 + 31598= 18274 + Show More4958 + 31598= 495 + 31598= 36548= 18274×22= 18274×1= 18274

Solving equation 13 for variable X3 we get,
 X3 = 60988  Ans. ... 14 + Show More66X3 = 18274Dividing both sides of the above equation by same number,⇒ [66X3] ÷ [66] = [18274] ÷ [66]⇒ X3 = 60988+ Show MoreL.H.S.= [66X3]÷66= [66X3÷66]= X3 + Show More66X3÷66= [66÷66]X3= 1X3 + Show More66 ÷ 66= 66×166= 1×661×11×66= 1×661×11×66= 11×11= 1R.H.S.= [18274]÷66= [18274÷66]= 60988 + Show More18274÷66= 60988 + Show More18274 ÷ 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 MoreSubstituting the following equation, X3 = 60988into- 274X2 + 32X3 = - 454we have,⇒  - 274X2 + 32×[60988] =  - 454⇒ - 274X2 + 1827176 = - 454+ Show MoreL.H.S.=  - 274X2 + 32×[60988]= - 274X2 + [32×60988]= - 274X2 + 1827176+ Show More60988×32= 1827176 + Show More60988×32= 609×388×2= 1827176R.H.S.=  - 454Subtracting same quantity from both sides of the above equation,⇒ [- 274X2 + 1827176] - [1827176] = [- 454] - [1827176]⇒ - 274X2 = - 3807176+ Show MoreL.H.S.= - 274X2 + 1827176 - 1827176= - 274X2 + 0+ Show More1827176 + -1827176= 0 + Show More1827176 + -1827176= 1827 + (-1827)176= 0176= 0R.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= -3807176Dividing both sides of the above equation by same number,⇒ [- 274X2] ÷ [- 274] = [- 3807176] ÷ [- 274]⇒ X2 = 14144+ Show MoreL.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= 1×-271×4×1×41×-27= 11×11= 1R.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×-2744×4×1×41×-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 MoreSubstituting the following equations, X3 = 60988X2 = 14144into52X1 + 32X2 + 3X3 = 854we have,⇒ 52X1 + 32×[14144] + 3×[60988] = 854⇒ 52X1 + 112544 = 854+ Show MoreL.H.S.= 52X1 + 32×[14144] + 3×[60988]= 52X1 + [32×14144] + [3×60988]= 52X1 + 42388 + 182788+ Show MoreSimplification 1:14144×32= 42388 + Show More14144×32= 141×344×2= 42388Simplification 2:60988×3= 182788 + Show More14144×32= 141×344×2= 42388= 52X1 + 112544+ Show More42388 + 182788= 112544 + Show More42388 + 182788= 423 + 182788= 225088= 112544×22= 112544×1= 112544R.H.S.= 854Subtracting same quantity from both sides of the above equation,⇒ [52X1 + 112544] - [112544] = [854] - [112544]⇒ 52X1 = - 9522+ Show MoreL.H.S.= 52X1 + 112544 - 112544= 52X1 + 0+ Show More112544 + -112544= 0 + Show More112544 + -112544= 1125 + (-1125)44= 044= 0R.H.S.= 854 - 112544= - 9522+ Show More854 + -112544= -9522 + Show More854 + -112544= 85×44 + (-1125)×44×44= 3740+(-4500)176= -760176= -9522×88= -9522×1= -9522Dividing both sides of the above equation by same number,⇒ [52X1] ÷ [52] = [- 9522] ÷ [52]⇒ X1 = - 1911+ Show MoreL.H.S.= [52X1]÷52= [52X1÷52]= X1 + Show More52X1÷52= [52÷52]X1= 1X1 + Show More52 ÷ 52= 52×25= 1×51×2×1×21×5= 1×51×2×1×21×5= 11×11= 1R.H.S.= [- 9522]÷52= [-9522÷52]= - 1911 + Show More-9522÷52= -1911 + Show More-9522 ÷ 52= -9522×25= -19×511×2×1×21×5= -19×511×2×1×21×5= -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 MoreSubstituting the following equations, X3 = 60988X2 = 14144X1 = - 1911intoX1 + 72X2 + X3 + 2X4 - 2X5 = - 3we have,⇒ 1×[- 1911] + 72×[14144] + 1×[60988] + 2X4 - 2X5 =  - 3⇒ 144488 + 2X4 - 2X5 = - 3+ Show MoreL.H.S.= 1×[- 1911] + 72×[14144] + 1×[60988] + 2X4 - 2X5= [1×-1911] + [72×14144] + [1×60988] + 2X4 - 2X5= - 1911 + 98788 + 60988 + 2X4 - 2X5+ Show MoreSimplification 1:-1911×1= -1911 + Show More-1911×1= (-19)×111×1= -1911Simplification 2:14144×72= 98788 + Show More-1911×1= (-19)×111×1= -1911Simplification 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= 36122R.H.S.=  - 3Subtracting same quantity from both sides of the above equation,⇒ [144488 + 2X4 - 2X5] - [144488] = [- 3] - [144488]⇒ 2X4 - 2X5 = - 42722+ Show MoreL.H.S.= 144488 + 2X4 - 2X5 - 144488= 0 + 2X4 - 2X5+ Show More144488 + -144488= 0 + Show More144488 + -144488= 1444 + (-1444)88= 088= 0R.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= -42722Dividing both sides of the above equation by same number,⇒ [2X4 - 2X5] ÷ [- 1] = [- 42722] ÷ [- 1]⇒ - 2X4 + 2X5 = 42722+ Show MoreL.H.S.= [2X4 - 2X5]÷-1= [2X4÷-1] + [-2X5÷-1]= - 2X4 + 2X5 + Show MoreSimplification 1:2X4÷(-1)= [2÷(-1)]X4= -2X4 + Show More2 ÷ (-1)= 2×1-1= -2×-1-1= -2×1= -2Simplification 2:(-2)X5÷(-1)= [(-2)÷(-1)]X5= 2X5 + Show More(-2) ÷ (-1)= (-2)×1-1= 2×-1-1= 2×1= 2R.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 MoreSubstituting the following equations, X3 = 60988X2 = 14144X1 = - 1911intoX1 + X2 + 4X3 - 12X4 - 2X5 = 17we have,⇒ 1×[- 1911] + 1×[14144] + 4×[60988] - 12X4 - 2X5 = 17⇒ 128344 - 12X4 - 2X5 = 17+ Show MoreL.H.S.= 1×[- 1911] + 1×[14144] + 4×[60988] - 12X4 - 2X5= [1×-1911] + [1×14144] + [4×60988] - 12X4 - 2X5= - 1911 + 14144 + 60922 - 12X4 - 2X5+ Show MoreSimplification 1:-1911×1= -1911 + Show More-1911×1= (-19)×111×1= -1911Simplification 2:14144×1= 14144 + Show More-1911×1= (-19)×111×1= -1911Simplification 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= 128344R.H.S.= 17Subtracting same quantity from both sides of the above equation,⇒ [128344 - 12X4 - 2X5] - [128344] = [17] - [128344]⇒ - 12X4 - 2X5 = - 53544+ Show MoreL.H.S.= 128344 - 12X4 - 2X5 - 128344= 0 - 12X4 - 2X5+ Show More128344 + -128344= 0 + Show More128344 + -128344= 1283 + (-1283)44= 044= 0R.H.S.= 17 - 128344= - 53544+ Show More17 + -128344= -53544 + Show More17 + -128344= 17×44 + (-1283)×144= 748+(-1283)44= -53544Dividing both sides of the above equation by same number,⇒ [- 12X4 - 2X5] ÷ [- 1] = [- 53544] ÷ [- 1]⇒ 12X4 + 2X5 = 53544+ Show MoreL.H.S.= [- 12X4 - 2X5]÷-1= [-12X4÷-1] + [-2X5÷-1]= 12X4 + 2X5 + Show MoreSimplification 1:-12X4÷(-1)= [-12÷(-1)]X4= 12X4 + Show More-12 ÷ (-1)= -12×1-1= 12×-1-1= 12×1= 12Simplification 2:(-2)X5÷(-1)= [(-2)÷(-1)]X5= 2X5 + Show More(-2) ÷ (-1)= (-2)×1-1= 2×-1-1= 2×1= 2R.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 MoreL.H.S.= [12X4 + 2X5]×4= [12X4×4] + [2X5×4]= 2X4 + 8X5 + Show MoreSimplification 1:12X4×4= [12×4]X4= 2X4 + Show More12×4= 11×2×2×21= 11×2×2×21= 11×21= 2Simplification 2:2X5×4= [2×4]X5= 8X5 + Show More2×4= 8R.H.S.= [53544]×4= [53544×4]= 53511 + Show More53544×4= 53511 + Show More53544×4= 53511×4×1×41= 53511×4×1×41= 53511×11= 53511

Adding these two equations we get,

 -2X4 + 2X5 = 42722 (+) 2X4 + 8X5 = 53511 + 10X5 = 149722 + Show MoreL.H.S.= [- 2X4 + 2X5] + [2X4 + 8X5]= - 2X4 + 2X5 + 2X4 + 8X5= - 2X4 + 2X4 + 2X5 + 8X5= 0 + 10X5+ Show MoreSimplification 1:(-2)X4 + 2X4= [(-2) + 2]X4= 0X4 + Show More-2 + 2= 0Simplification 2:2X5 + 8X5= [2 + 8]X5= 10X5 + Show More2 + 8= 10= 10X5R.H.S.= [42722] + [53511]= 42722 + 53511= 149722+ Show More42722 + 53511= 149722 + Show More42722 + 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 More10X5 = 149722Dividing both sides of the above equation by same number,⇒ [10X5] ÷ [10] = [149722] ÷ [10]⇒ X5 = 1497220+ Show MoreL.H.S.= [10X5]÷10= [10X5÷10]= X5 + Show More10X5÷10= [10÷10]X5= 1X5 + Show More10 ÷ 10= 10×110= 1×101×11×10= 1×101×11×10= 11×11= 1R.H.S.= [149722]÷10= [149722÷10]= 1497220 + Show More149722÷10= 1497220 + Show More149722 ÷ 10= 149722×110= 1497220
Substituting the value of variable X5 from equation 19 into 17 we get,
 X4 = - 2910  Ans. ... 20 + Show MoreSubstituting the following equation, X5 = 1497220into- 2X4 + 2X5 = 42722we have,⇒  - 2X4 + 2×[1497220] = 42722⇒ - 2X4 + 1497110 = 42722+ Show MoreL.H.S.=  - 2X4 + 2×[1497220]= - 2X4 + [2×1497220]= - 2X4 + 1497110+ Show More1497220×2= 1497110 + Show More1497220×2= 1497110×2×1×21= 1497110×2×1×21= 1497110×11= 1497110R.H.S.= 42722Subtracting same quantity from both sides of the above equation,⇒ [- 2X4 + 1497110] - [1497110] = [42722] - [1497110]⇒ - 2X4 = 295+ Show MoreL.H.S.= - 2X4 + 1497110 - 1497110= - 2X4 + 0+ Show More1497110 + -1497110= 0 + Show More1497110 + -1497110= 1497 + (-1497)110= 0110= 0R.H.S.= 42722 - 1497110= 295+ Show More42722 + -1497110= 295 + Show More42722 + -1497110= 427×110 + (-1497)×2222×110= 46970+(-32934)2420= 140362420= 295×484484= 295×1= 295Dividing both sides of the above equation by same number,⇒ [- 2X4] ÷ [- 2] = [295] ÷ [- 2]⇒ X4 = - 2910+ Show MoreL.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= 1×-21×11×-2= 11×11= 1R.H.S.= [295]÷-2= [295÷-2]= - 2910 + Show More295÷(-2)= -2910 + Show More295 ÷ (-2)= 295×1-2= -2910×-1-1= -2910×1= -2910