How do you solve the system of equations -2x - 3y = 7 and x + 8y = - 36?

1 Answer
Morgan S.
Dec 2, 2017

y=-5\quad,\quad x=4

Explanation:

We’ll use elimination for this problem by first cancelling out the x terms, so we can solve for y.

Given the equations:

-2x-3y=7

x+8y=-36

We can multiply the bottom equation by 2, so 2x and -2x will be eliminated:

2(x+8y)=(-36)2

\implies color(red)(2x)+16y=-72

Adding it to the other equation:

cancel(color(red)(-2x))-3y=7\quad+\quad cancel(color(red)(2x))+16y=-72

\implies 13y=-65

\implies y-=5

Now we can plug y into one of the equations to solve for x:

-2x-3y=7

\implies -2x-3(-5)=7

\implies -2x+15=7

#\implies -2x=-8

\implies x=4

Finally, to check our answers, we can plug both x and y into an equation:

x+8y=-36

#\implies 4+8(-5)=-36

\implies 4-40=-36

\implies -36=-36

So the answer is correct.

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