Question

Which of the following points is a solution to the system of equations y=1/2x−2
and y=3/2x−4
?(1 point)
Responses

(2, -1)
(2, -1)

(-2, -3)
(-2, -3)

(1, -1.5)
(1, -1.5)

(-1, -2.5)
(-1, -2.5)

Answer 1

To determine which points are solutions to the system of equations \(y = \frac{1}{2}x - 2\) and \(y = \frac{3}{2}x - 4\), we can substitute each point into both equations and see if they satisfy both.

1. **Point (2, -1)**:
- For \(y = \frac{1}{2}(2) - 2\):
\[
y = 1 - 2 = -1 \quad (\text{True})
\]
- For \(y = \frac{3}{2}(2) - 4\):
\[
y = 3 - 4 = -1 \quad (\text{True})
\]
- **Point (2, -1) is a solution**.

2. **Point (-2, -3)**:
- For \(y = \frac{1}{2}(-2) - 2\):
\[
y = -1 - 2 = -3 \quad (\text{True})
\]
- For \(y = \frac{3}{2}(-2) - 4\):
\[
y = -3 - 4 = -7 \quad (\text{False})
\]
- **Point (-2, -3) is not a solution**.

3. **Point (1, -1.5)**:
- For \(y = \frac{1}{2}(1) - 2\):
\[
y = 0.5 - 2 = -1.5 \quad (\text{True})
\]
- For \(y = \frac{3}{2}(1) - 4\):
\[
y = 1.5 - 4 = -2.5 \quad (\text{False})
\]
- **Point (1, -1.5) is not a solution**.

4. **Point (-1, -2.5)**:
- For \(y = \frac{1}{2}(-1) - 2\):
\[
y = -0.5 - 2 = -2.5 \quad (\text{True})
\]
- For \(y = \frac{3}{2}(-1) - 4\):
\[
y = -1.5 - 4 = -5.5 \quad (\text{False})
\]
- **Point (-1, -2.5) is not a solution**.

**Conclusion**: The only point that is a solution to the system of equations is **(2, -1)**.