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:

Solve linear equations using substitution or elimination methods.

Answer 1

The Correct Option is A

Solving by substitution or elimination:
Multiply the second equation by 2:
\[ 4x - 4y = 4 \] Adding to the first equation: \[ 3x + 4y + 4x - 4y = 10 + 4 \] \[ 7x = 14 \Rightarrow x = 2. \] Substituting in \( 3(2) + 4y = 10 \): \[ 6 + 4y = 10 \Rightarrow 4y = 4 \Rightarrow y = 1. \]