Question

Use substitution to solve the system of equations.

y = 2x + 16
2x – 7y = –64

Question 6 options:

(–4, 8)

(–1, 11)

(8, –4)

(–7, –11)

Answer 1

(-4, 8)

Explanation:

The two equations in the system are:
`\left \{ {{y=2x+16} \atop {2x-7y=-64}} \right`

We are asked to use substitution, so we select the first equation as our substitution equation, since we have it already expressed in the form that indicates what the unknown "y" is in terms of the unknown "x" (y=2x+16)

we can therefore substitute the "y" in the second equation by "2x+16" and convert the equation into one that can be solved with only one unknown (x):

`2x-7y=-64\\2x-7(2x+16)=-64\\2x-14x-112=-64\\-12x=112-64\\-12x=48\\x=(48)/(-12) \\x=-4`

Now that we have the value for "x", we can use it in the first equation (the one we use as substitution) to find what y is:

`y=2x+16\\y=2(-4)+16\\y=-8+16\\y=8`

Then, the pair: x = -4 and y = 8 is our solution. We write it in coordinate pair form as: (-4, 8)