Question

Solve for $x$: $3x+7y=32$ and $7x+3y=48$.

Answer 1

Given equations are,

$3x+7y=32$ .....(1)
and $7x+3y=48$ .....(2)
Step 1: Adding both the equations, we get

$10x+10y=80$

$\Rightarrow 10(x+y)=10\times 8$
$\Rightarrow x+y=8$ .....(3)
Step 2: Subtracting equation (1) from equation (2),

$(7x+3y)-(3x+7y)=48-32$
$\Rightarrow 4x-4y=16$

$\Rightarrow 4(x-y)=4\times 4$

$\Rightarrow x-y=4$ .......(4)
Step 3: Adding equations (3) and (4), we get
$x+y+x-y=12$

$\Rightarrow 2x=12$

$\Rightarrow x=6$
Substituting $x=6$ in any of the equations (1), we get $y=2$

$\therefore$ the solutions of the pair of equations is $x=6$ and $y=2$.