Question

Write four solutions for the given equation:
$x=6y$

Answer 1

Finding four solution for the equation $x=6y$:

The given equation will be written as;

$x-6y+0=0$$·····\left(i\right)$

Putting $y=0$in equation $\left(i\right)$

we get, $x-6\left(0\right)+0=0$

$\Rightarrow x=0$

Thus, $\left(0,0\right)$ is a solution of equation $\left(i\right)$.

Putting $x=6$ in equation $\left(i\right)$,

$\Rightarrow 6-6y+0=0$

$\Rightarrow 6=6y$

$\Rightarrow y=1$

Thus, $\left(6,1\right)$ is a solution of equation $\left(i\right)$.

Putting $x=2$ in equation $\left(i\right)$

$\Rightarrow 2-6y+0=0$

$\Rightarrow 2=6y$

$\Rightarrow y=\frac{1}{3}$

Thus, $\left(2,\frac{1}{3}\right)$ is a solution of equation $\left(i\right)$

Putting $y=\frac{1}{2}$ in equation $\left(i\right)$

$\Rightarrow x-6\left(\frac{1}{2}\right)+0=0$

$\Rightarrow x-3=0$

$\Rightarrow x=3$

Thus, $\left(3,\frac{1}{2}\right)$ is a solution of equation $\left(i\right)$.

Therefore, $\left(0,0\right),\left(6,1\right),\left(2,\frac{1}{3}\right),\left(3,\frac{1}{2}\right)$ are four solution to equation $x-6y+0=0$.