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How do you solve the following system?: $2 x - 9 y = - 3, - x + y = 8$ $2x -9y =-3 , -x +y = 8$

1 Answer

Nov 26, 2015

$x = - \frac{69}{7}$ $x=-69/7$ ; $y = - \frac{13}{7}$ $y=-13/7$

Explanation:

Given
[1] $XXX 2 x - 9 y = - 3$ $color(white)("XXX")2x-9y=-3$
[2] $XXX - x + y = 8$ $color(white)("XXX")-x+y=8$

[2] $\times 9 \to$ $xx 9 rarr$
$XXX$ $color(white)("XXX")$ [3] $XXX - 9 x + 9 y = 72$ $color(white)("XXX")-9x+9y=72$

[1] $+$ $+$ [3] $\to$ $rarr$
$XXX$ $color(white)("XXX")$ [4] $XXX - 7 x = 69$ $color(white)("XXX")-7x=69$

[4] $\div (- 7) \to$ $div (-7) rarr$
$XXX$ $color(white)("XXX")$ [5] $XXX x = - \frac{69}{7}$ $color(white)("XXX")x=-69/7$

[2] $\times 2 \to$ $xx 2 rarr$
$XXX$ $color(white)("XXX")$ [6] $XXX - 2 x + 2 y = 16$ $color(white)("XXX")-2x+2y=16$

[1] $+$ $+$ [6] $\to$ $rarr$
$XXX$ $color(white)("XXX")$ [7] $XXX - 7 y = 13$ $color(white)("XXX")-7y = 13$

[7] $\div (- 7) \to$ $div (-7) rarr$
$XXX$ $color(white)("XXX")$ [8] $XXX y = - \frac{13}{7}$ $color(white)("XXX")y=-13/7$

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