Question

A pair of equations is shown below.

3x − y = 9
y = −2x + 11

If the two equations are graphed, at what point do the lines representing the two equations intersect? (4 points)

Group of answer choices

(4, 3)

(3, 4)

(9, 11)

(11, 9)

Answer 1

Answer: (4,3)

Explanation:

We can rearrange the first equation to get
`3x-9=y`.

Thus, we can conclude that:

• 3x - 9 = -2x + 11
• 5x - 9 = 11 [add 2x to both sides]
• 5x = 20 [add 9 to both sides]
• x = 4 [divide both sides by 5]

Thus, if x = 4, y=3(4)-9=3.

So, they graphs intersect at (4,3).