Question

If the solutions of ax + by = 2 and bx+y=5 are 4, 6 then a =

• A. \(\frac{-1}{4}\)
• B. \(\frac{7}{8}\)
• C. \(\frac{-3}{4}\)
• D. \(\frac{-7}{8}\)

Answer 1

The Correct Option is B

We are given that the pair \( (x, y) = (4, 6) \) is a solution to both equations: 1) \( ax + by = 2 \) \\ 2) \( bx + y = 5 \) \\ Substitute \( x = 4, y = 6 \) into the second equation: \[ b(4) + 6 = 5 \Rightarrow 4b = -1 \Rightarrow b = -\frac{1}{4} \] Now substitute \( x = 4, y = 6 \) into the first equation: \[ a(4) + \left(-\frac{1}{4}\right)(6) = 2 \Rightarrow 4a - \frac{6}{4} = 2 \Rightarrow 4a = 2 + \frac{3}{2} = \frac{7}{2} \] Solving for \( a \): \[ a = \frac{7}{2 \times 4} = \frac{7}{8} \]

The correct option is (B): \(\frac{7}{8}\)