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How do you solve the following system using substitution?: $- 2 x + 5 y = - 2, x - 3 y = 3$ $-2x+5y=-2, x-3y=3$

1 Answer

Oct 26, 2015

Re-write one of the equations into the form
$XXX x = an expression$ $color(white)("XXX")x= "an expression"$
then substitute the "expression" for $x$ $x$ in the other equation.
$XXX (x, y) = (- 9, - 4)$ $color(white)("XXX")(x,y)=(-9,-4)$

Explanation:

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

Rearranging the terms of [2]
[3] $XXX x = 3 y + 3$ $color(white)("XXX")x=3y+3$

Substituting $3 y + 3$ $3y+3$ for $x$ $x$ in [1]
[4] $XXX - 2 (3 y + 3) + 5 y = - 2$ $color(white)("XXX")-2(3y+3)+5y = -2$

Simplifying
[5] $XXX - 6 y - 6 + 5 y = - 2$ $color(white)("XXX")-6y-6+5y=-2$

[6] $XXX y = - 4$ $color(white)("XXX")y=-4$

Substituting $(- 4)$ $(-4)$ for $y$ $y$ in [2]
[7] $XXX x - 3 (- 4) = 3$ $color(white)("XXX")x-3(-4)=3$

[8] $XXX x = - 9$ $color(white)("XXX")x=-9$

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