Questions: For question I determine which of the following ordered pairs satisfy each system of linear equations. Prove your answers for each pair ijy showing work. 1) y=4 x-2 2 x+3 y=8 a) (0,-2) b) (4,0) C) (1,2)

Solution Steps

To determine which ordered pairs satisfy the given system of linear equations, substitute each pair into both equations and check if both equations hold true. If both equations are satisfied for a pair, then that pair is a solution to the system.

We will substitute each ordered pair \((x, y)\) into the equations \(y = 4x - 2\) and \(2x + 3y = 8\) to check if they satisfy both equations.

For the pair \((0, -2)\):

1. Substitute into the first equation: \[ -2 = 4(0) - 2 \implies -2 = -2 \quad \text{(True)} \]
2. Substitute into the second equation: \[ 2(0) + 3(-2) = 8 \implies 0 - 6 = 8 \implies -6 = 8 \quad \text{(False)} \] Thus, \((0, -2)\) is not a solution.

For the pair \((4, 0)\):

1. Substitute into the first equation: \[ 0 = 4(4) - 2 \implies 0 = 16 - 2 \implies 0 = 14 \quad \text{(False)} \]
2. Since the first equation is false, we do not need to check the second equation. Thus, \((4, 0)\) is not a solution.

For the pair \((1, 2)\):

1. Substitute into the first equation: \[ 2 = 4(1) - 2 \implies 2 = 4 - 2 \implies 2 = 2 \quad \text{(True)} \]
2. Substitute into the second equation: \[ 2(1) + 3(2) = 8 \implies 2 + 6 = 8 \implies 8 = 8 \quad \text{(True)} \] Thus, \((1, 2)\) is a solution.

Final Answer