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How do you solve $6 x + 5 y = - 12$ $6x + 5y = -12$ and $- 9 x + y = 69$ $-9x + y = 69$ using substitution?

1 Answer

Jul 9, 2016

$(x, y) = (- 7, 6)$ $(x,y)=color(blue)(""(-7,6))$

Explanation:

Given
[1] $XXX 6 x + 5 y = - 12$ $color(white)("XXX")6x+5y=-12$
[2] $XXX - 9 x + y = 69$ $color(white)("XXX")-9x+y=69$

re-arranging [1]
[3] $XXX y = 9 x + 69$ $color(white)("XXX")y=9x+69$

substituting $(9 x + 69)$ $(9x+69)$ from [3] for $y$ $y$ in [1]
[4] $XXX 6 x + 5 (9 x + 69) = - 12$ $color(white)("XXX")6x+5(9x+69)=-12$

simplifying
[5] $XXX 51 x + 345 = - 12$ $color(white)("XXX")51x+345=-12$

[6] $XXX 51 x = - 357$ $color(white)("XXX")51x=-357$

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

substituting $(- 7)$ $(-7)$ for $x$ $x$ in [3]
[8] $XXX y = 9 \cdot (- 7) + 69 = 6$ $color(white)("XXX")y=9*(-7)+69=6$

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