Question

Which of the order pairs are solutions to the equation

Answer 1

Given the expression:

`y=(1)/(3)x+1`

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:

`\begin{gathered} y=(1)/(3)\cdot(-6)+1 \\ y=-(6)/(3)+1 \\ y=-2+1 \\ y=-1 \end{gathered}`

The solution is (-6, -1) and the ordered pair is (-6, -1). Thus (-6, -1) is a solution.

b) (9, 4).

`\begin{gathered} y=(1)/(3)\cdot9+1 \\ y=(9)/(3)+1 \\ y=3+1 \\ y=4 \end{gathered}`

The solution is (9, 4) and the ordered pair is (9, 4). Thus (9, 4) is a solution.

c) (-3, 0).

`\begin{gathered} y=(1)/(3)\cdot(-3)+1 \\ y=-(3)/(3)+1 \\ y=-1+1 \\ y=0 \end{gathered}`

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.