Question

If \( 2a + 3b = 8 \) and \( 3a - 4b = -5 \), then the values of \( a \) and \( b \) are:

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

Hint:

For solving a system of linear equations, use the elimination or substitution method.

Answer 1

The Correct Option is A

We solve the system of equations:
\[ 2a + 3b = 8 \quad \cdots (1) \] \[ 3a - 4b = -5 \quad \cdots (2) \] Step 1: Multiply equation (1) by 3 and equation (2) by 2 to align coefficients of \( a \):
\[ 6a + 9b = 24 \] \[ 6a - 8b = -10 \] Step 2: Subtract the second equation from the first:
\[ (6a + 9b) - (6a - 8b) = 24 - (-10) \] \[ 17b = 34 \] \[ b = 2 \] Step 3: Substitute \( b = 2 \) in equation (1):
\[ 2a + 3(2) = 8 \] \[ 2a + 6 = 8 \] \[ 2a = 2 \] \[ a = 1 \] Thus, \( a = 1, b = 2 \).