The image shows the graph of the system of linear equations {y=2x+2y=2x−4

Question

{
𝑦
=
2
𝑥
+
2
𝑦
=
2
𝑥
−
4
. Which of the following points, if any, are solutions to the system of equations?

(1 point)
Responses

(0,−4)
(
0
,
−
4
)
open paren 0 comma negative 4 close paren

Neither of these points are solutions.
Neither of these points are solutions.

(0,2)
(
0
,
2
)
open paren 0 comma 2 close paren

Both of these points are solutions.

Answer 1

To determine which points, if any, are solutions to the system of equations:

1. $y=2x+2$
2. $y=2x-4$

We can substitute the points to see if they satisfy both equations.

Check the point $(0,-4)$:

Substituting $x=0$ and $y=-4$ into both equations:

1. First equation:
   $y=2(0)+2$
   $-4=2$ → Not true.

2. Second equation:
   $y=2(0)-4$
   $-4=-4$ → True.

Since this point only satisfies the second equation and not the first, $(0,-4)$ is not a solution for the system.

---

Check the point $(0,2)$:

Substituting $x=0$ and $y=2$ into both equations:

1. First equation:
   $y=2(0)+2$
   $2=2$ → True.

2. Second equation:
   $y=2(0)-4$
   $2=-4$ → Not true.

Since this point only satisfies the first equation and not the second, $(0,2)$ is not a solution for the system.

---

Since neither point is a solution, the correct response is:

Neither of these points are solutions.