Question

Write four solutions for the following equations: $2x+y=7$

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, $2x+y=7$

Substitute $x=0$,

$$\begin{gathered} 2\left(0\right)+y=7 \\ \Rightarrow y=7 \end{gathered}$$

Substitute $x=1$,

$$\begin{gathered} 2\left(1\right)+y=7 \\ \Rightarrow y=7-2 \\ \Rightarrow y=5 \end{gathered}$$

Substitute $x=2$,

$$\begin{gathered} 2\left(2\right)+y=7 \\ \Rightarrow y=7-4 \\ \Rightarrow y=3 \end{gathered}$$

Substitute $x=3$,

$$\begin{gathered} 2\left(3\right)+y=7 \\ \Rightarrow y=7-6 \\ \Rightarrow y=1 \end{gathered}$$

Hence, the four solutions are $(0,7),(1,5),(2,3)\mathrm{and}(3,1)$.