Question

Solve the following simultaneous equations by the method of equating coefficients.$5x+7y=17;7x+5y=19$

• A. $x=1,y=1$
• B. $x=4,y=1$
• C. $x=3,y=1$
• D. $x=2,y=1$

Answer 1

The correct option is D $x=2,y=1$

$5x+7y=17$ ...(i)

$7x+5y=19$ ...(ii)

On multiplying (i) by 7 and (ii) by 5, we get

$35x+49y=119$
$\underset{–}{\underset{-}{3}5x\underset{-}{+}25y=\underset{-}{9}5}$
$24y=24$

$\therefore y=1$

On putting $y=1$ in (i), we get

$5x+7\left(1\right)=17$

$\Rightarrow x=2$

$\therefore x=2,y=1$