Solve the system of equations
y=2x+4
y=x^2+x-2

The two intersections would be (3, 10) and (-2, 0)

Step-by-step explanation:

To solve this system of equations, set the two equations equal to each other and solve for x.

2x + 4 = x^2 + x - 2

2x = x^2 + x - 6

0 = x^2 - x - 6

0 = (x - 3)(x + 2)

Now set the parenthesis equal to zero to get the x values.

x - 3 = 0

x = 3

x + 2 = 0

x = -2

Now we know the x values of each interception. We can find the y values by plugging into either equation.

y = 2x + 4

y = 2(3) + 4

y = 6 + 4

y = 10

y = 2x + 4

y = 2(-2) + 4

y = -4 + 4

y = 0

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