Question

If \(3x-2y=12\) and \(4x-5y=16\), then

• A. \(x=4,\ y=0\)
• B. \(x=0,\ y=4\)
• C. \(x=4,\ y=2\)
• D. \(x=1,\ y=10\)

Hint:

To solve two linear equations, align coefficients (by multiplication) and subtract to eliminate one variable.

Answer 1

The Correct Option is A

Step 1: Eliminate \(y\).
Multiply \(3x-2y=12\) by \(5\): \(15x-10y=60\).
Multiply \(4x-5y=16\) by \(2\): \(8x-10y=32\).
Step 2: Subtract equations.
\((15x-10y)-(8x-10y)=60-32 \Rightarrow 7x=28 \Rightarrow x=4.\)
Step 3: Back-substitute.
\(3(4)-2y=12 \Rightarrow 12-2y=12 \Rightarrow y=0.\)