Question

Write four solutions for the given equation:

$x+\mathrm{\pi y}=4$

Answer 1

Finding four solution for equation $x+\mathrm{\pi y}=4$:

The given equation will be written as;

$x+\mathrm{\pi }y-4=0$$·····\left(i\right)$

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

we get, $x+\mathrm{\pi }\left(0\right)-4=0$

$\Rightarrow x=4$

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

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

$\Rightarrow 0+\mathrm{\pi }y-4=0$

$\Rightarrow \mathrm{\pi y}=4$

$\Rightarrow y=\frac{4}{\mathrm{\pi }}$

Thus, $\left(0,\frac{4}{\mathrm{\pi }}\right)$ is a solution of equation $\left(i\right)$.

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

$\Rightarrow 1+\mathrm{\pi }y-4=0$

$\Rightarrow \mathrm{\pi y}=3$

$\Rightarrow y=\frac{3}{\mathrm{\pi }}$

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

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

$\Rightarrow x+\mathrm{\pi }\left(\frac{2}{\mathrm{\pi }}\right)-4=0$

$\Rightarrow x+2=4$

$\Rightarrow x=2$

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

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