Question

Write four solutions for the following equations: $x=4y$

Answer 1

Solutions of an equation:

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, $x=4y$

Substitute $x=0$,

$$\begin{gathered} 0=4y \\ \Rightarrow y=\frac{0}{4} \\ \Rightarrow y=0 \end{gathered}$$

Substitute $x=4$,

$$\begin{gathered} 4=4y \\ \Rightarrow y=\frac{4}{4} \\ \Rightarrow y=1 \end{gathered}$$

Substitute $x=16$,

$$\begin{gathered} 16=4y \\ \Rightarrow y=\frac{16}{4} \\ \Rightarrow y=4 \end{gathered}$$

Substitute $x=-4$,

$$\begin{gathered} -4=4y \\ \Rightarrow y=\frac{4}{-4} \\ \Rightarrow y=-1 \end{gathered}$$

Hence, the four solutions are $(0,0),(4,1),(16,4)\mathrm{and}(-4,-1)$.