Question

If \( 3x + 4y = 10 \) and \( 2x - 2y = 2 \), then:

• A. \( x = 2, y = 1 \)
• B. \( x = 1, y = 2 \)
• C. \( x = -1, y = -2 \)
• D. \( x = 3, y = 1 \)

Hint:

To solve a system of equations, solve one equation for one variable and substitute into the other.

Answer 1

The Correct Option is A

We are given the system of equations: \[ 3x + 4y = 10 \quad \text{(1)}, \] \[ 2x - 2y = 2 \quad \text{(2)}. \] First, solve equation (2) for \( x \): \[ 2x = 2 + 2y \quad \Rightarrow \quad x = 1 + y. \] Substitute this into equation (1): \[ 3(1 + y) + 4y = 10 \quad \Rightarrow \quad 3 + 3y + 4y = 10 \quad \Rightarrow \quad 7y = 7 \quad \Rightarrow \quad y = 1. \] Substitute \( y = 1 \) into \( x = 1 + y \): \[ x = 1 + 1 = 2. \] Thus, \( x = 2 \) and \( y = 1 \), so the solution is \( \boxed{x = 2, y = 1} \).