X1 | + | X2 | + | 4X3 | - | - | 2X5 | = | 17 | ... 1 | ||
X1 | + | + | X3 | + | 2X4 | - | 2X5 | = | -3 | ... 2 | + Show More Simplifying, ⇒ X1 + ⇒ X1 + L.H.S. = X1 + = X1 + = [ = = = = 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 + ⇒ X1 + L.H.S. = X1 + = X1 + (-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 | |
+ | + | 3X3 | = | ... 3 | ||||||||
2X1 | - | + | 3X3 | = | ... 4 | |||||||
5X1 | - | X2 | + | 2X3 | = | 2 | ... 5 |
+ | + | 3X3 | = | ... 6 | Same as 3 | |||||||
2X1 | - | + | 3X3 | = | ... 7 | Same as 4 | ||||||
5X1 | - | X2 | + | 2X3 | = | 2 | ... 8 | Same as 5 | ||||
X1 | + | + | X3 | + | 2X4 | - | 2X5 | = | -3 | ... 9 | Same as 2 | |
X1 | + | X2 | + | 4X3 | - | - | 2X5 | = | 17 | ... 10 | Same as 1 |
- | ... 11 | + Show More We have,
Multiplying the first and second equations by -2 and
Adding these two equations we get,
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... 12 | + Show More We have,
Multiplying the first and second equations by -5 and 2 respectively we get,
Adding these two equations we get,
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66X3 = | ... 13 | + Show More We have,
Multiplying the first and second equations by
Adding these two equations we get,
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X3 = | ... 14 | + Show More 66X3 = Dividing both sides of the above equation by same number, ⇒ [66X3] ÷ [66] = [ ⇒ X3 = L.H.S. = [66X3]÷66 = [66X3÷66] = X3 + Show More 66X3÷66 = [66÷66]X3 = 1X3 + Show More 66 ÷ 66 = 66× = = = = 1 R.H.S. = [ = [ = = = = = = = |
X2 = | ... 15 | + Show More Substituting the following equation, X3 = into - we have, ⇒ - ⇒ - L.H.S. = - = - = - = = = R.H.S. = - Subtracting same quantity from both sides of the above equation, ⇒ [- ⇒ - L.H.S. = - = - = 0 + Show More = = = 0 R.H.S. = - = - = = = = = = = Dividing both sides of the above equation by same number, ⇒ [- ⇒ X2 = L.H.S. = [- = [ = X2 + Show More = [ = 1X2 + Show More = = = = = 1 R.H.S. = [- = [ = = = = = = = |
X1 = - | ... 16 | + Show More Substituting the following equations, X3 = X2 = into we have, ⇒ ⇒ L.H.S. = = = Simplification 1: = = = Simplification 2: = = = = = = = = = = R.H.S. = Subtracting same quantity from both sides of the above equation, ⇒ [ ⇒ L.H.S. = = = 0 + Show More = = = 0 R.H.S. = = - = = = = = = = Dividing both sides of the above equation by same number, ⇒ [ ⇒ X1 = - L.H.S. = [ = [ = X1 + Show More = [ = 1X1 + Show More = = = = = 1 R.H.S. = [- = [ = - = = = = = = |
-2X4 | + | 2X5 | = | ... 17 | + Show More Substituting the following equations, X3 = X2 = X1 = - into X1 + we have, ⇒ 1×[- ⇒ L.H.S. = 1×[- = [1× = - Simplification 1: = = = Simplification 2: = = = Simplification 3: = = = = - = = = = = = = R.H.S. = - 3 Subtracting same quantity from both sides of the above equation, ⇒ [ ⇒ 2X4 - 2X5 = - L.H.S. = = 0 + 2X4 - 2X5+ Show More = 0 + Show More = = = 0 R.H.S. = - 3 - = - (-3) + = -3 + = = = = = = Dividing both sides of the above equation by same number, ⇒ [2X4 - 2X5] ÷ [- 1] = [- ⇒ - 2X4 + 2X5 = 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× = -2× = -2×1 = -2 Simplification 2: (-2)X5÷(-1) = [(-2)÷(-1)]X5 = 2X5 + Show More (-2) ÷ (-1) = (-2)× = 2× = 2×1 = 2 R.H.S. = [- = [ = = = = = = | |
+ | 2X5 | = | ... 18 | + Show More Substituting the following equations, X3 = X2 = X1 = - into X1 + X2 + 4X3 - we have, ⇒ 1×[- ⇒ L.H.S. = 1×[- = [1× = - Simplification 1: = = = Simplification 2: = = = Simplification 3: = = = = - = = = = R.H.S. = 17 Subtracting same quantity from both sides of the above equation, ⇒ [ ⇒ - L.H.S. = = 0 - = 0 + Show More = = = 0 R.H.S. = 17 - = - 17 + = 17 + = = = Dividing both sides of the above equation by same number, ⇒ [- ⇒ L.H.S. = [- = [ = Simplification 1: = [ = = = = = Simplification 2: (-2)X5÷(-1) = [(-2)÷(-1)]X5 = 2X5 + Show More (-2) ÷ (-1) = (-2)× = 2× = 2×1 = 2 R.H.S. = [- = [ = = = = = = |
10X5 = | ... 19 | + Show More We have,
Multiplying the second equation by 4 we get,
Adding these two equations we get,
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X5 = | ... 19 | + Show More 10X5 = Dividing both sides of the above equation by same number, ⇒ [10X5] ÷ [10] = [ ⇒ X5 = L.H.S. = [10X5]÷10 = [10X5÷10] = X5 + Show More 10X5÷10 = [10÷10]X5 = 1X5 + Show More 10 ÷ 10 = 10× = = = = 1 R.H.S. = [ = [ = = = = |
X4 = - | ... 20 | + Show More Substituting the following equation, X5 = into - 2X4 + 2X5 = we have, ⇒ - 2X4 + 2×[ ⇒ - 2X4 + L.H.S. = - 2X4 + 2×[ = - 2X4 + [2× = - 2X4 + = = = = = R.H.S. = Subtracting same quantity from both sides of the above equation, ⇒ [- 2X4 + ⇒ - 2X4 = L.H.S. = - 2X4 + = - 2X4 + 0+ Show More = 0 + Show More = = = 0 R.H.S. = = = = = = = = = Dividing both sides of the above equation by same number, ⇒ [- 2X4] ÷ [- 2] = [ ⇒ X4 = - L.H.S. = [- 2X4]÷-2 = [-2X4÷-2] = X4 + Show More (-2)X4÷(-2) = [(-2)÷(-2)]X4 = 1X4 + Show More (-2) ÷ (-2) = (-2)× = = = = 1 R.H.S. = [ = [ = - = = = = = |