Question

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

Answer 1

Solutions of an equations:

The solutions of the equations are the values that satisfy the given equation.

To find the four solutions, substitute any value of $x$ and then find corresponding values of $y$.

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

Substitute $x=0$,

$$\begin{gathered} \mathrm{\pi }\left(0\right)+y=9 \\ \Rightarrow y=9 \end{gathered}$$

Substitute $x=1$,

$$\begin{gathered} \mathrm{\pi }\left(1\right)+y=9 \\ \Rightarrow y=9-\mathrm{\pi } \end{gathered}$$

Substitute $x=2$,

$$\begin{gathered} \mathrm{\pi }\left(2\right)+y=9 \\ \Rightarrow y=9-2\mathrm{\pi } \end{gathered}$$

Substitute $x=3$,

$$\begin{gathered} \mathrm{\pi }\left(3\right)+y=9 \\ \Rightarrow y=9-3\mathrm{\pi } \end{gathered}$$

Hence, the four solutions are $(0,9),(1,9-\mathrm{\pi }),(2,9-2\mathrm{\pi })\mathrm{and}(3,9-3\mathrm{\pi })$.