Question

If $29x+37y=103$, $37x+29y=95$, then

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

Answer 1

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

Given equations are
$29x+37y=103$ ...$\left(i\right)$
$37x+29y=95$ ...$\left(ii\right)$
On multiplying $\left(i\right)$ by $37$ and $\left(ii\right)$ by $29$ and subtracting, we get
$1073x+1369y=3811$
$\underset{–}{\underset{-}{1}073x\underset{-}{+}841y=\underset{-}{2}755}$
$528y=1056$
$\therefore y=2$
On putting $y=2$ in $\left(i\right)$, we get
$29x=103-37\times \left(2\right)\Rightarrow 29x=29$
$\therefore x=1$
$\therefore x=1,y=2$
Hence, option $A$ is correct.