Question

Determine if (-2,6) and (4,12) are solutions to the system of equations:

y = x + 8
2y = x^2 + 8​

Answer 1

Both
`(-2,6)` and
`(4,12)` are solutions to the system.

Explanation:

In order to determine whether the two given points represent solutions to our system of equations, we must "plug" thos points into both equations and check that the equality remains valid.

Step 1: Plug
`(-2,6)` into
`y=x+8`

`(6) = (-2)+8 = 6`

The solution verifies the equation.

Step 2: Plug
`(-2,6)` into
`2y=x^2 + 8`

`2(6) = (-2)^2+8=4+8=12`

The solution verifies both equations. Therefore,
`(-2,6)` is a solution to this system.

Now we must check if the second point is also valid.

Step 3: Plug
`(4,12)` into
`y=x+8`

`(12) = (4)+8 = 12`

Step 4: Plug
`(4,12)` into
`2y=x^2 + 8`

`2(12) = (4)^2+8=16+8=24`

The solution verifies both equations. Therefore,
`(4,12)` is another solution to this system.