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How do you solve the following system using substitution?: $x - 3 y = 2, x + y = - 10$ $x-3y=2, x+y=-10$

1 Answer

Oct 21, 2015

$(x, y) = (- 7, - 3)$ $(x,y) = (-7,-3)$

Explanation:

Given
[1] $XXX x - 3 y = 2$ $color(white)("XXX")x-3y=2$
[2] $XXX x + y = - 10$ $color(white)("XXX")x+y=-10$

Rearrange [1], isolating $x$ $x$ on one side:
[3] $XXX x = 3 y + 2$ $color(white)("XXX")x=3y+2$

Substitute $(3 y + 2)$ $(3y+2)$ for $x$ $x$ in [2]
[4] $XXX (3 y + 2) + y = - 10$ $color(white)("XXX")(3y+2)+y=-10$

Simplify
[5] $XXX 4 y = - 12$ $color(white)("XXX")4y=-12$

[6] $XXX y = - 3$ $color(white)("XXX")y=-3$

Substitute $(- 3)$ $(-3)$ for $y$ $y$ in [1]
[7] $XXX x - 3 (- 3) = 2$ $color(white)("XXX")x-3(-3) = 2$

[8] $XXX x + 9 = 2$ $color(white)("XXX")x+9 = 2$

[9] $XXX x = - 7$ $color(white)("XXX")x=-7$

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