Question

How do you find the ordered pair that satisfies 3x-2y=-4 and x+2y=12?

Answer 1

`color(red)("The ordered pair is (2,5).")`

One way is to use the method of elimination.

Step 1. Enter the equations.

[1] `3x-2y=-4`
[2] `x+2y=12`

Step 2. Add Equations 1 and 2.

`4x=8`

[3] `x=2`

Step 3. Substitute Equation 3 in Equation 2.

`x+2y=12`
`2+2y=12`
`2y=10`
`y=5`

Solution: The ordered pair that satisfies the equations is (`2,5`).

Check: Substitute the values of `x` and `y` in Equation 1.

`3x-2y=-4`
`3×2-2×5 = -4`
`6-10=-4`
`-4=-4`

It checks!

Our solution is correct.