Given the expression:
[tex]y=\frac{1}{3}x+1[/tex]
To find the order pairs that are the solution of this equation, substitute x and find y. Then verify if the y found is the same as the y in the ordered pair.
a) (-6, -1).
Substituting x by -6:
[tex]\begin{gathered} y=\frac{1}{3}\cdot(-6)+1 \\ y=-\frac{6}{3}+1 \\ y=-2+1 \\ y=-1 \end{gathered}[/tex]
The solution is (-6, -1) and the ordered pair is (-6, -1). Thus (-6, -1) is a solution.
b) (9, 4).
[tex]\begin{gathered} y=\frac{1}{3}\cdot9+1 \\ y=\frac{9}{3}+1 \\ y=3+1 \\ y=4 \end{gathered}[/tex]
The solution is (9, 4) and the ordered pair is (9, 4). Thus (9, 4) is a solution.
c) (-3, 0).
[tex]\begin{gathered} y=\frac{1}{3}\cdot(-3)+1 \\ y=-\frac{3}{3}+1 \\ y=-1+1 \\ y=0 \end{gathered}[/tex]
The solution is (-3, 0) and the ordered pair is (-3, 0). Thus (-3, 0) is a solution.
In summary,
The order pairs (-6, -1), (9, 4) and (-3, 0) are solutions of the equation.
