Question

Which point is a solution to the system of linear equations?

y = −x + 4

x − 3y = 12?
(0, 3)
(1, 2)
(6, −2)
(4, −4)

Answer 1

To determine which point is a solution to the system of equations given by

1. \(y = -x + 4\)
2. \(x - 3y = 12\)

we can substitute each point into both equations.

**Let's check each point:**

1. **Point (0, 3):**
- For the first equation:
\[
y = -x + 4 \implies 3 = -0 + 4 \implies 3 = 4 \quad \text{(not true)}
\]
- Thus, (0, 3) is not a solution.

2. **Point (1, 2):**
- For the first equation:
\[
y = -x + 4 \implies 2 = -1 + 4 \implies 2 = 3 \quad \text{(not true)}
\]
- Thus, (1, 2) is not a solution.

3. **Point (6, -2):**
- For the first equation:
\[
y = -x + 4 \implies -2 = -6 + 4 \implies -2 = -2 \quad \text{(true)}
\]
- Now, check the second equation:
\[
x - 3y = 12 \implies 6 - 3(-2) = 12 \implies 6 + 6 = 12 \implies 12 = 12 \quad \text{(true)}
\]
- Thus, (6, -2) is a solution.

4. **Point (4, -4):**
- For the first equation:
\[
y = -x + 4 \implies -4 = -4 + 4 \implies -4 = 0 \quad \text{(not true)}
\]
- Thus, (4, -4) is not a solution.

**Conclusion: The point (6, -2) is a solution to the system of linear equations.**