Question

The system of equations shown below is graphed on a coordinate grid:

3y + x = 4
2y − x = 6

Which statement is true about the coordinates of the point that is the solution to the system of equations?
It is (−2, 2) and lies on both lines.
It is (−5, 3) and lies on both lines.
It is (−5, 3) and does not lie on either line.
It is (−2, 2) and does not lie on either line.

Answer 1

Your answer would be the first option, (-2, 2).

We can solve this system of equations by adding them together, as the +x and -x will cancel:

3y + x = 4

+2y - x = 6

5y = 10

y = 2

Now we can find the x value by substituting the y value into one of the equations:

3(2) + x = 4

6 + x = 4

x = -2

Therefore your answer is (-2, 2). We know that it is the first option and not the last option because the point (-2, 2) does lie on both lines as it satisfies both equations when substituted in.

I hope this helps!

Answer 2

A) (-2,2) lies on both lines

Explanation: