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

Question

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.