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How do you solve $8 x = - 2 y - 10$ $8x = -2y - 10$ and $2 x = 4 y$ $2x = 4y$ using substitution?

1 Answer

May 10, 2016

$(x, y) = (- \frac{10}{9}, - \frac{5}{9})$ $(x,y)=color(blue)(""(-10/9,-5/9))$

Explanation:

Given:
[1] $XXX 8 x = - 2 y - 10$ $color(white)("XXX")8x=-2y-10$
[2] $XXX 2 x = 4 y$ $color(white)("XXX")2x=4y$

Dividing both sides of [2] by 2
[3] $XXX x = 2 y$ $color(white)("XXX")x=2y$

From [3] we see that we can substitute $2 y$ $2y$ anywhere for $x$ $x$
and specifically we can substitute $2 y$ $2y$ for $x$ $x$ in [1] to get
[4] $XXX 8 (2 y) = - 2 y - 10$ $color(white)("XXX")8(2y)=-2y-10$

Simplifying:
[5] $XXX 16 y = - 2 y - 10$ $color(white)("XXX")16y=-2y-10$

[6] $XXX 18 y = - 10$ $color(white)("XXX")18y=-10$

[7] $XXX y = - \frac{5}{9}$ $color(white)("XXX")y=-5/9$

We can now substitute $(- \frac{5}{9})$ $(-5/9)$ for $y$ $y$ in [3] to get
[8] $XXX x = 2 (- \frac{5}{9}) = - \frac{10}{9}$ $color(white)("XXX")x=2(-5/9)=-10/9$

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