Question

The image shows the graph of the system of linear equations {y = 2x + 2. Which of the following points, {y = 2x - 4. if any, are solutions to the system of equations?

A: Neither of these points are solutions

B: Both of these points are solutions.

C: ( 0,2 )

D: ( 0, -4)

Answer 1

To determine whether the points \( (0, 2) \) and \( (0, -4) \) are solutions to the system of equations \( y = 2x + 2 \) and \( y = 2x - 4 \), we can evaluate each point in both equations.

1. **For the point \( (0, 2) \)**:
- Substitute \( x = 0 \) into the first equation:
\[
y = 2(0) + 2 = 2
\]
- So, \( (0, 2) \) satisfies the first equation.
- Now, substitute \( x = 0 \) into the second equation:
\[
y = 2(0) - 4 = -4
\]
- So, \( (0, 2) \) does not satisfy the second equation.

2. **For the point \( (0, -4) \)**:
- Substitute \( x = 0 \) into the first equation:
\[
y = 2(0) + 2 = 2
\]
- So, \( (0, -4) \) does not satisfy the first equation.
- Now, substitute \( x = 0 \) into the second equation:
\[
y = 2(0) - 4 = -4
\]
- So, \( (0, -4) \) satisfies the second equation.

In summary:
- \( (0, 2) \): satisfies \( y = 2x + 2 \) but not \( y = 2x - 4 \).
- \( (0, -4) \): satisfies \( y = 2x - 4 \) but not \( y = 2x + 2 \).

Neither of the points are solutions to the entire system of equations. Therefore, the answer is:

**A: Neither of these points are solutions.**