Question

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

Answer 1

`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.