Question

Write four solutions for the given equation:

$\frac{2}{3}x-y=4$

Answer 1

Finding four solution for equation :$\frac{2}{3}x-y=4$

The given equation will be written as;

$\frac{2}{3}x-y-4=0$$·····\left(i\right)$

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

we get, $\frac{2}{3}x-0-4=0$

$\Rightarrow x=\frac{12}{2}=6$

Thus, $\left(6,0\right)$ is a solution of equation $\left(i\right)$.

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

$\Rightarrow \frac{2}{3}\left(0\right)-y-4=0$

$\Rightarrow y=-4$

Thus, $\left(0,-4\right)$ is a solution of equation $\left(i\right)$.

Putting $x=3$ in equation $\left(i\right)$

$\Rightarrow \frac{2}{3}\left(3\right)-y-4=0$

$\Rightarrow 2-4=y$

$\Rightarrow y=-2$

Thus, $\left(3,-2\right)$ is a solution of equation $\left(i\right)$

Putting $y=-1$ in equation $\left(i\right)$

$\Rightarrow \frac{2}{3}x-\left(-1\right)-4=0$

$\Rightarrow \frac{2}{3}x=4-1$

$\Rightarrow x=\frac{9}{2}$

Thus, $\left(\frac{9}{2},-1\right)$ is a solution of equation $\left(i\right)$.

Therefore, $\left(6,0\right),\left(0,-4\right),\left(3,-2\right),\left(\frac{9}{2},-1\right)$ are four solution of equation $\frac{2}{3}x-y=4$.