Question

Solve the following simultaneous equations:

$217x+131y=913$
$131x+217y=827$

• A. $x=7,y=3$
• B. $x=2,y=1$
• C. $x=3,y=2$
• D. $x=1,y=5$

Answer 1

The correct option is C $x=3,y=2$

$217x+131y=913$ ...$\left(i\right)$
$131x+217y=827$ ...$\left(ii\right)$
On multiplying $\left(i\right)$ by $131$ and $\left(ii\right)$ by $217$ and subtracting, we get
$28427x+17161y=119603$
$\underset{–}{\underset{-}{2}8427x\underset{-}{+}47089y=\underset{-}{1}79459}$
$-29928y=-59856$
$\therefore y=2$
On putting $y=2$ in $\left(i\right)$, we get
$217x+131\times 2=913\Rightarrow 217x=651\Rightarrow x=3$
$\therefore x=3,y=2$