Question

The point (5, -3) is a solution to which system of equations? (2
2 y = x + 6 3
3y + 6x - 18 = 0
y=x-8
2x + y = 7
1 y=-x+6
y = 3x-1
y = x + 2
y = x + 5

Answer 1

To determine which system of equations has the point (5, -3) as a solution, we need to substitute the x-coordinate (5) and the y-coordinate (-3) into each equation and see which one(s) hold true.

Let's evaluate each equation one by one:

1. **Equation:** \(2y = x + 6\)
- Substitute \(x = 5\) and \(y = -3\):
\[
2(-3) = 5 + 6 \implies -6 = 11 \quad \text{(False)}
\]

2. **Equation:** \(3y + 6x - 18 = 0\)
- Substitute \(x = 5\) and \(y = -3\):
\[
3(-3) + 6(5) - 18 = 0 \implies -9 + 30 - 18 = 0 \implies 3 = 0 \quad \text{(False)}
\]

3. **Equation:** \(y = x - 8\)
- Substitute \(x = 5\):
\[
-3 = 5 - 8 \implies -3 = -3 \quad \text{(True)}
\]

4. **Equation:** \(2x + y = 7\)
- Substitute \(x = 5\) and \(y = -3\):
\[
2(5) + (-3) = 7 \implies 10 - 3 = 7 \implies 7 = 7 \quad \text{(True)}
\]

5. **Equation:** \(y = -x + 6\)
- Substitute \(x = 5\):
\[
-3 = -5 + 6 \implies -3 = 1 \quad \text{(False)}
\]

6. **Equation:** \(y = 3x - 1\)
- Substitute \(x = 5\):
\[
-3 = 3(5) - 1 \implies -3 = 15 - 1 \implies -3 = 14 \quad \text{(False)}
\]

7. **Equation:** \(y = x + 2\)
- Substitute \(x = 5\):
\[
-3 = 5 + 2 \implies -3 = 7 \quad \text{(False)}
\]

8. **Equation:** \(y = x + 5\)
- Substitute \(x = 5\):
\[
-3 = 5 + 5 \implies -3 = 10 \quad \text{(False)}
\]

The equations that are true with the point (5, -3) are:

- \(y = x - 8\)
- \(2x + y = 7\)

Therefore, the point (5, -3) is a solution to the system of equations consisting of \(y = x - 8\) and \(2x + y = 7\).