Question

Write four solutions for each of the following equations: $\mathrm{\pi }x+y=9$

Answer 1

Find the solutions for the given equation

Given equation is, $\mathrm{\pi }x+y=9$

Let $x=0$
$\begin{array}{cc}\Rightarrow & \mathrm{\pi }\left(0\right)+\mathrm{y}=9\\ \Rightarrow & y=9\end{array}$

Thus, $\left(0,9\right)$ is a solution for the given equation

Let $y=0$
$\begin{array}{cc}\Rightarrow & \mathrm{\pi }x+0=9\\ \Rightarrow & x=\frac{9}{\mathrm{\pi }}\end{array}$

Thus, $\left(\frac{\mathrm{\pi }}{9},0\right)$ is a solution for the given equation

Let $x=2$
$\begin{array}{cc}\Rightarrow & \mathrm{\pi }\left(2\right)+y=9\\ \Rightarrow & y=\frac{9}{2\mathrm{\pi }}\end{array}$

Thus, $\left(2,\frac{9}{2\mathrm{\pi }}\right)$ is a solution for the given equation

Let $y=1$
$\begin{array}{cc}\Rightarrow & \mathrm{\pi }x+1=9\\ \Rightarrow & x=\frac{8}{\mathrm{\pi }}\end{array}$

Thus, $\left(\frac{8}{\mathrm{\pi }},1\right)$ is a solution for the given equation

Therefore, $\left(0,9\right)$, $\left(\frac{\mathrm{\pi }}{9},0\right)$, $\left(2,\frac{9}{2\mathrm{\pi }}\right)$, and $\left(\frac{8}{\mathrm{\pi }},1\right)$ are the four solutions of the given equation.