Question

If \( 2a + 3b = 8 \) and \( 3a - 4b = -5 \), then

• A. \( a = 1, b = 2 \)
• B. \( a = 2, b = 1 \)
• C. \( a = -1, b = 2 \)
• D. \( a = 2, b = -2 \)

Hint:

To solve a system of linear equations, multiply the equations to align the coefficients of one variable and eliminate it by addition or subtraction.

Answer 1

The Correct Option is A

Step 1: Solve the system of equations: \[ 2a + 3b = 8 \quad \text{(1)} \] \[ 3a - 4b = -5 \quad \text{(2)} \] Step 2: Multiply equation (1) by 3 and equation (2) by 2 to eliminate \( a \): \[ 6a + 9b = 24 \quad \text{(3)} \] \[ 6a - 8b = -10 \quad \text{(4)} \] Step 3: Subtract equation (4) from equation (3): \[ (6a + 9b) - (6a - 8b) = 24 - (-10) \] \[ 17b = 34 \quad \Rightarrow \quad b = 2 \] Step 4: Substitute \( b = 2 \) into equation (1): \[ 2a + 3(2) = 8 \quad \Rightarrow \quad 2a + 6 = 8 \quad \Rightarrow \quad a = 1 \] Thus, the correct answer is \( a = 1, b = 2 \).