Question

Which ordered pair is a solution of the
equation?
-3x + 5y = 2x + 3y

Answer 1

Solve the equation for
`{y}`.

`y=(5x)/(2)`

Choose any value for
`{x}` that is in the domain to plug into the equation.

Choose
`{0}` to substitute in for
`{x}` to find the ordered pair.

`{(0,0)}`

Choose
`{1}` to substitute in for
`{x}` to find the ordered pair.

`(1,(5)/(2))`

Choose
`{2}` to substitute in for
`{x}` to find the ordered pair.

`{(2,5)}`

These are three possible solutions to the equation.

`{(0,0),}`
`(1,(5)/(2) )`,
`{(2,5)}`

Answer 2

Let’s set up steps to solve for the ordered pair.

1. Eliminate x on the left side

-3x + 5y + 3x = 2x + 3y + 3x

5y = 5x + 3y

2. Eliminate y on the right side

5y - 3y = 5x

2y = 5x

3. Divide both sides by the coefficient of y

2 / 2 = 1
5 / 2 = 5/2

4. Simplify

y = 5/2x

The ordered pair(s) representative of the solution to this equation would be (2, 5), (0, 0), or (1, 5/2).