Question

If \(2x + y = 35\) and \(3x + 4y = 65\), then the value of \(\frac{x}{y}\) is

• A. 2
• B. 3
• C. 5
• D. 4

Hint:

Use substitution or elimination method to solve simultaneous linear equations.

Answer 1

The Correct Option is C

We find the solution to the system of equations: \[ 2x + y = 35 \quad \text{and} \quad 3x + 4y = 65 \] Multiply the first equation by 4: \[ 8x + 4y = 140 \] Subtract the second equation: \[ (8x + 4y) - (3x + 4y) = 140 - 65 \] \[ 5x = 75 \quad \Rightarrow \quad x = 15 \] Substitute \(x = 15\) into \(2x + y = 35\): \[ 2(15) + y = 35 \quad \Rightarrow \quad y = 5 \] Therefore, \(\frac{x}{y} = \frac{15}{5} = 3\).