Question

Find three points that solve the equation X - 3y = -6

Answer 1

Given the linear equation:

`x-3y=-6`

The single linear equation above contains two variables. Hence, there is no unique solution but infinitely many pairs of solutions. For every value of x, there is a value for y.

Three points that solve the equation would be:

Solution 1

Put x = -6 into the equation

`\begin{gathered} -6-3y=-6 \\ -3y=-6+6 \\ (-3y)/(-3)=(0)/(-3) \\ y=0 \end{gathered}`

Solution 2

Put x = 0 into the equation

`\begin{gathered} 0-3y=-6 \\ -3y=-6 \\ (-3y)/(-3)=(-6)/(-3) \\ y=2 \end{gathered}`

Solution 3

Put x = 12 into the equation

`\begin{gathered} 12-3y=-6 \\ -3y=-6-12 \\ -3y=-18 \\ (-3y)/(-3)=(-18)/(-3) \\ y=6 \end{gathered}`

Therefore, three points that solve the linear equation as shown above are:

`\begin{gathered} (x,y)=(-6,0) \\ (x,y)=(0,2) \\ (x,y)=(12,6) \end{gathered}`