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

y = x + 8
2y = x^2 + 8​

User Philly
by
8.1k points

1 Answer

1 vote

Answer:

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.

User Vikingben
by
7.9k points

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