Question

If the following three equations hold simultaneously for $x$ and $y$, find p.
$3x-2y=6,\frac{x}{3}-\frac{y}{6}=\frac{1}{2},x-py=6$.

Answer 1

let us solve first 2 equations to finf $x$ and $y$ and the substitute it in third equation to find $p$

$3x-2y=6---eqn\left(1\right)$

$\frac{x}{3}-\frac{y}{6}=\frac{1}{2}$

Multiplying with LCM of $3$ and $6$ on both sides.

LCM of $3$ and $6$ is $6$

$2x-y=3---eqn\left(2\right)$

Multiplying $eqn\left(2\right)$ with 2

$4x-2y=6---eqn\left(3\right)$

then subtracting $eqn\left(3\right)$ from $eqn\left(1\right)$ we get $x=0$.

Substituting $x=0$ in $eqn\left(1\right)$ we get $y=-3$

Substituting $x=0$ and $y=-3$ in $x-py=6$

$\Rightarrow$ $0-p\times (-3)=6$

$p=2$