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:
- \( y - 3x = -2 \)
- \( y = 4 \)
Let's evaluate each given point.
-
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: \[ y = 4 \quad (\text{satisfied}) \]
-
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: \[ y = 2 \quad (\text{not satisfied}) \]
-
Point (2, 4):
- Substitute into the first equation: \[ 4 - 3(2) = -2 \Rightarrow 4 - 6 = -2 \quad (\text{satisfied}) \]
- Check the second equation: \[ y = 4 \quad (\text{satisfied}) \]
-
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 \((2, 4)\).
1 answer