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if 2x y 35 and 3x 4y 65 then the value of frac x y
Question:
If \(2x + y = 35\) and \(3x + 4y = 65\), then the value of \(\frac{x}{y}\) is
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Use substitution or elimination method to solve simultaneous linear equations.
JEECUP - 2024
JEECUP
Updated On:
Jun 6, 2025
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C
Solution and Explanation
We solve the system of equations: \[ 2x + y = 35 \quad \text{and} \quad 3x + 4y = 65 \] Multiplying the first equation by 4: \[ 8x + 4y = 140 \] Subtracting the second equation: \[ (8x + 4y) - (3x + 4y) = 140 - 65 \] \[ 5x = 75 \quad \Rightarrow \quad x = 15 \] Substitute \(x = 15\) into \(2x + y = 35\): \[ 2(15) + y = 35 \quad \Rightarrow \quad y = 5 \] Thus, \(\frac{x}{y} = \frac{15}{5} = 3\).
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