Question

Solve the following pair of equations:

$41x+53y=135$
$53x+41y=147$

• A. $x=2;y=1$
• B. $x=1;y=4$
• C. $x=2;y=7$
• D. $x=3;y=-4$

Answer 1

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

Given

$41x+53y=135$ ...$\left(1\right)$

$53x+41y=147$ ...$\left(2\right)$

Multiply equation $\left(1\right)$ by $41$ and $\left(2\right)$ by $53$

We get

$1681x+2173y=5535$ ...$\left(3\right)$

$2809x+2173y=7791$ ...$\left(4\right)$

Subtract $\left(4\right)$ with $\left(3\right)$ we get

$1138x=2256$

Or $x=2$

Put the value of $x=2$ in equation $\left(1\right)$ we get

$41\times 2+53y=135$

$\Rightarrow 82+53y=135$

$\Rightarrow 53y=147-82$

$\Rightarrow 53y=53$

$\Rightarrow y=1$

Then $x=2$ and $y=1$