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How do you solve -4x+y=-11 and 2x-3y=5?

1 Answer

Nov 30, 2015

$(x, y) = (\frac{14}{5}, \frac{1}{5})$ $(x,y) = (14/5,1/5)$

Explanation:

Given:
[1] $XXX - 4 x + y = - 11$ $color(white)("XXX")-4x+y=-11$
[2] $XXX 2 x - 3 y = 5$ $color(white)("XXX")2x-3y=5$

Multiply [2] by $2$ $2$ giving $x$ $x$ a coefficient of the same magnitude as in [1]
[3] $XXX 4 x - 6 y = 10$ $color(white)("XXX")4x-6y =10$

Add [1] and [3], eliminating the $x$ $x$ term
[4] $XXX - 5 y = - 1$ $color(white)("XXX")-5y = -1$

Divide both sides of [4] by $(- 5)$ $(-5)$
[6] $XXX y = \frac{1}{5}$ $color(white)("XXX")y=1/5$

Multiply [1] by $3$ $3$ giving $y$ $y$ a coefficient of the same magnitude as in [2]
[7] $XXX - 12 x + 3 y = - 33$ $color(white)("XXX")-12x+3y=-33$

Add [2] and [7], eliminating the $y$ $y$ term
[8] $XXX - 10 x = - 28$ $color(white)("XXX")-10x = -28$

Divide both sides of [8] by $(- 10)$ $(-10)$
[9] $XXX x = \frac{14}{5}$ $color(white)("XXX")x=14/5$

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