How do you solve $9x-9y=-27$ and $5x+27=y$ using substitution?

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Answer 1 · 2017-02-09T22:05:51

See the entire solution process below:

Step 1) Because the second equation is already solved for $y$ , substitute $5x + 27$ for $y$ in the first equation and solve for $x$ :

$9x - 9y = -27$ becomes:

$9x - 9(5x + 27) = -27$

$9x - 45x - 243 = -27$

$-36x - 243 = -27$

$-36x - 243 + color(red)(243) = -27 + color(red)(243)$

$-36x - 0 = 216$

$-36x = 216$

$(-36x)/color(red)(-36) = 216/color(red)(-36)$

$(color(red)(cancel(color(black)(-36)))x)/cancel(color(red)(-36)) = -6$

$x = -6$

Step 2) Substitute $-6$ for $x$ in the second equation and calculate $y$ :

$5x + 27 = y$ becomes:

$(5 xx -6) + 27 = y$

$-30 + 27 = y$

$-3 = y$

$y = -3$

The solution is $x = -6$ and $y = -3$ or $(-6, -3)$

How do you solve 9x-9y=-279x-9y=-27 and 5x+27=y5x+27=y using substitution?