Question

Solve the equation, using the domain of x = {-1, 0, 2}.
2x + 3y = 7

Answer 1

You simply plug in the allowed x values and get the corresponding y-values.
Ex: when x=-1 you have
2(-1) +3y=7
-2+3y=7
3y=9
y=3 so you have the solution (-1, 3)


When x=0
2(0)+3y=7
3y=7
y=7/3
So you have the solution (0, 7/3)

When x=2
2(2)+3y=7
4+3y=7
3y=3
y=1
So you have the solution (2, 1)

Or another way to write this is y={3, 7/3, 1}
The fancy brackets { } denote a set of numbers
So y={3, 7/3, 1} is your range (range is the allowed values of y)

Answer 2

Or, solve the equation for y first:
\[2x + 3y = 7 \rightarrow y=\frac{7-2x}{3}.\]
Then input your domain:
\[y=\frac{7-2\left \{-1, 0, 2 \right \}}{3}\]
and evaluate.