Question

Solve the following simultaneous equations by elimination method and find the value of $x$ $5y-3x=14;3y-2x=1$

Answer 1

Given equations are,

$5y-3x=14$ .........(1)
$3y-2x=1$ ..........(2)

Multiply (1) by $2$ and (2) by $3$ we get,

$10y-6x=28$ .........(3)
$9y-6x=3$ ..........(4)

Subtracting (4) from (3) we get,

$(10y-6x)-(9y-6x)=28-3$
$\Rightarrow y=25$

Substituting $y=25$ in (1) we get,

$5\times 25-3x=14$

$\Rightarrow 125-3x=14$

$\Rightarrow -3x=14-125$

$\Rightarrow -3x=-111$
$\Rightarrow x=37$

Hence, the value of $x$ is $37$