Question

Find the ordered pairs for the equation -10x - y = -20.

Answer 1

Let's begin by listing out the information given to us:

`\begin{gathered} -10x-y=-20 \\ Since\text{ all the elements have a negative parenthesis, multiply by -1} \\ -10x(-1)-y(-1)=-20(-1) \\ 10x+y=20 \end{gathered}`

We proceed by rearranging the equation to be in the standard form (y = ax + b), we have:

`\begin{gathered} 10x+y=20 \\ \text{Subtract 10x from both side, we have:} \\ 10x-10x+y=-10x+20 \\ y=-10x+20 \end{gathered}`

To get the ordered pairs, we will choose values for x; x = -3, 0, 2. We have:

`\begin{gathered} y=-10x+20 \\ x=-3 \\ y=-10(-3)+20=30+20 \\ y=50 \\ (x,y)=(-3,50) \\ \\ x=0 \\ y=-10(0)+20=0+20 \\ y=20 \\ (x,y)=(0,20) \\ \\ x=2 \\ y=-10(2)+20=-20+20 \\ y=0 \\ (x,y)=(2,0) \end{gathered}`

We thus have the following ordered pairs: (x, y) = (-3, 50); (0, 20); (2, 0)