Question

If \(3x – 4y = 1\) and \(5x – 6y = 7,\) then \(x+y\) =

Answer 1

Given,
\(3x – 4y = 1...(i)\)
\(5x – 6y = 7...(ii)\)

To make the coefficients of x equal, multiply equation (1) by 5 and equation (2) by 3.

\(Equation (1) \times 5 \Rightarrow \\15x – 20y = 5...(iii)\)

\(Equation (2) \times 3 \Rightarrow \\15x – 18y = 21 ...(iv)\)

(iv) - (iii)
\(\Rightarrow~2y = 21-5 =16\)
\(\Rightarrow y = 8\)

Substitute the value of y in (i) \(3x - 4\times8 = 1\)
\(3x = 33 \\ \Rightarrow x = 11\)

\(\Rightarrow x + y =11+8=19\)