Question

Examine this system of linear equations.

y – 3x = –2,

y = 4

Which is a solution of the system of equations?
(0, 4)
(2, 2)
(2, 4)
(4, 2)

Answer 1

To determine which point is a solution of the system of equations, we will substitute each point into both equations to see if they satisfy both equations.

The system of equations is:

1. \( y - 3x = -2 \)
2. \( y = 4 \)

Let's evaluate each given point.

1. **Point (0, 4)**:
- Substitute into the first equation:
\[
4 - 3(0) = -2 \Rightarrow 4 \neq -2 \quad (\text{not a solution})
\]
- Check the second equation:
\[
y = 4 \quad (\text{satisfied})
\]

2. **Point (2, 2)**:
- Substitute into the first equation:
\[
2 - 3(2) = -2 \Rightarrow 2 - 6 = -4 \quad (\text{not a solution})
\]
- Check the second equation:
\[
y = 2 \quad (\text{not satisfied})
\]

3. **Point (2, 4)**:
- Substitute into the first equation:
\[
4 - 3(2) = -2 \Rightarrow 4 - 6 = -2 \quad (\text{satisfied})
\]
- Check the second equation:
\[
y = 4 \quad (\text{satisfied})
\]

4. **Point (4, 2)**:
- Substitute into the first equation:
\[
2 - 3(4) = -2 \Rightarrow 2 - 12 = -10 \quad (\text{not a solution})
\]
- Check the second equation:
\[
y = 2 \quad (\text{not satisfied})
\]

After testing all points, only **(2, 4)** satisfies both equations.

Thus, the solution to the system of equations is \((2, 4)\).