Question

If $3x–4y=1$ and $5x–6y=7,$ then $x+y$ = ___.

• A. 16
• B. 20
• C. 18
• D. 19

Answer 1

The correct option is D 19

Given,
$3x–4y=\mathrm{1...}\left(i\right)$
$5x–6y=\mathrm{7...}\left(ii\right)$

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

$Equation\left(1\right)\times 5\Rightarrow 15x–20y=\mathrm{5...}\left(iii\right)$

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

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

Substitute the value of y in (i) $3x-4\times 8=1$
$3x=33\Rightarrow x=11$

$\Rightarrow x+y=11+8=19$