Question

Use elimination method for solving the following equations:
$41x+53y=135$, $53x+41y=147$

Answer 1

Given equations are:

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

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

Multiply equation (1) by $41$ and equation (2) by $53$ we get,

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

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

Subtract equations (3) from equation (4) to eliminate $y$,

$1128x=2256$

$\Rightarrow x=2$

Substitute this value of $x$ in equation (1), we get

$41\left(2\right)+53y=135$

$\Rightarrow 82+53y=135$

$\Rightarrow 53y=135-82$

$\Rightarrow 53y=53$

$\Rightarrow y=1$

Therefore, the solution is $x=2,y=1$.