Question

Use the system of equations to answer the question.



2
x
−
y
=
2

y
=
2
3
x
+
1



Which graph shows this system of equations?

A.
image


B.
image


C.
image


D.
image

Answer 1

First put both equations in slope-intercept form.

From 2x − y = 2: y = 2x − 2 (slope 2, y-intercept −2).
The second is y = (2/3)x + 1 (slope 2/3, y-intercept 1).

So look for the graph that has:
- One line passing through (0, −2) and (1, 0) (steeper, slope 2).
- The other line passing through (0, 1) and (3, 3) (shallower, slope 2/3).
- They intersect at (9/4, 5/2) = (2.25, 2.5).

Compare the four images and pick the option that matches those intercepts/slopes/intersection. If you can upload or describe the four graphs I’ll pick the correct letter.