Questions: Determine whether the given set of ordered pairs (a) (1,4), (b) (-1,-5), and (c) (-3,-9) are solutions of the system of equations. 2x - y = 3 -8x + 4y = -12 (c) Is (-3,-9) a solution of the system? Choose the correct answer below. A. Yes, because it satisfies the first equation. B. Yes, because it satisfies both the equations. C. No, because it does not satisfy at least one equation. D. No, because it satisfies both the equations.

Solution Steps

For the ordered pair \( (1, 4) \):

• Substitute into the first equation: \[ 2(1) - 4 = 2 - 4 = -2 \quad (\text{not equal to } 3) \]
• Substitute into the second equation: \[ -8(1) + 4(4) = -8 + 16 = 8 \quad (\text{not equal to } -12) \] Thus, \( (1, 4) \) is not a solution.

For the ordered pair \( (-1, -5) \):

• Substitute into the first equation: \[ 2(-1) - (-5) = -2 + 5 = 3 \quad (\text{equal to } 3) \]
• Substitute into the second equation: \[ -8(-1) + 4(-5) = 8 - 20 = -12 \quad (\text{equal to } -12) \] Thus, \( (-1, -5) \) is a solution.

For the ordered pair \( (-3, -9) \):

• Substitute into the first equation: \[ 2(-3) - (-9) = -6 + 9 = 3 \quad (\text{equal to } 3) \]
• Substitute into the second equation: \[ -8(-3) + 4(-9) = 24 - 36 = -12 \quad (\text{equal to } -12) \] Thus, \( (-3, -9) \) is a solution.

Final Answer