Question

Which ordered pair is a solution to the system of linear equations?

x + 4y = 6
y = −4x − 6

A: (−2, −2)

B: (−2, 2)

C: (2, 2)

D: (2, −2)

Answer 1

B: (-2, 2)

Explanation:

We can solve this equation using substitution:

x+4y=6

4y=6-x

y=
`(-x)/(4)`+
`(3)/(2)`

y=-4x-6

So, since y equals both of these expressions, the expressions must be equal.

`(-x)/(4)`+
`(3)/(2)` = -4x-6

`(15x)/(4)`=
`(-15)/(2)`

x=
`(-15)/(2)`*
`(4)/(15)`=-2

y= -4x-6 = -4(-2) - 6 = 8-6 = 2

x=-2

y=2

The ordered pair is (-2, 2), which is choice B.

Hope this helps! :)

Since this is multiple choice, you can also plug in each ordered pair into the equations with the x and y values, but when it is open response, substitution is a good option.

Answer 2

Answer: B (-2, 2)

Explanation:

You substitute the values of the variables into each equation to see if they are both true.

(-2) + 4(2) = 6

(-2) + 8 = 6

6 = 6

2 = -4(-2) - 6

2 = 8 - 6

2 = 2

When pulling in B to both equations, both are true!
So B is your answer.