Question

A system of equations is graphed.



image


Which TWO statements are TRUE?

A.
(
3
,
0
)
is a solution to the system.

B.
(
−
3
,
2
)
is a solution to the system.

C.
The equation
y
=
3
x
+
1
describes one of the lines in the system.

D.
The equation
y
=
2
3
x
+
4
describes one of the lines in the system.

E.
The equation
y
=
−
1
3
x
+
3
describes one of the lines in the system.

Answer 1

I can't see the graph you mention. Could you either upload the image or describe the two lines (their intercepts or two clear points on each line and the intersection point)?

To solve it yourself, use these quick checks:

- A / B (points): "A solution to the system" means the point where the two lines intersect. Check the graph to see the intersection coordinates; if it is (3, 0) then A is true; if it is (−3, 2) then B is true.

- C / D / E (equations): Identify one line by two grid points on it, then compute its slope (rise/run) and y-intercept. Compare to the provided equations:
- y = 3x + 1 has slope 3 and y-intercept 1
- y = (2/3)x + 4 has slope 2/3 and y-intercept 4
- y = −(1/3)x + 3 has slope −1/3 and y-intercept 3

If you upload the graph or tell me two points on each line (or the intersection point), I’ll pick the two true statements.