Question

The image shows the graph of the following system of linear equations: .
Which of the following points, if any, is a solution to the system?
(1 point)
{
y = x + 5
2
3
y = −x
(1, −1)
(2, 3)
(−3, 3)
(0, 5)

Answer 1

To determine which points are solutions to the system of equations given by:

1. \( y = x + 5 \)
2. \( y = -x \)

we need to check if the given points satisfy both equations.

1. **Check point (1, -1):**
- For \( y = x + 5 \):
\( -1 = 1 + 5 \) ⇒ False
- Thus, (1, -1) is **not** a solution.

2. **Check point (2, 3):**
- For \( y = x + 5 \):
\( 3 = 2 + 5 \) ⇒ False
- Thus, (2, 3) is **not** a solution.

3. **Check point (-3, 3):**
- For \( y = x + 5 \):
\( 3 = -3 + 5 \) ⇒ True
- For \( y = -x \):
\( 3 = -(-3) \) ⇒ True
- Thus, (-3, 3) **is a solution**.

4. **Check point (0, 5):**
- For \( y = x + 5 \):
\( 5 = 0 + 5 \) ⇒ True
- For \( y = -x \):
\( 5 = -0 \) ⇒ False
- Thus, (0, 5) is **not** a solution.

The only point that is a solution to the system of equations is **(-3, 3)**.