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Pls someone answer this quickly and with work and answer pls​

Pls someone answer this quickly and with work and answer pls​-example-1

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Answer:

The solutions (6, -2) and (2,2) satisfy both equations f(x) and g(x).

The solutions (2, 2) and (6, -2) are the two possible solutions of the system of equations. Geometrically, they represent the points of intersection between the parabola f(x) and the straight line g(x) on the x-y plane.

Explanation:

To solve the system of equations, we need to find the values of x that satisfy both equations f(x) and g(x).

Substitute g(x) into f(x) to eliminate one variable:

f(x) = -x^2 + 2x + 4

g(x) = -x + 4f(g(x)) = -(g(x))^2 + 2(g(x)) + 4

= -(x-4)^2 + 2(x-4) + 4

= -x^2 + 8x - 12

Now we have one equation in one variable:

-x^2 + 8x - 12 = 0

Solve for x using the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = -1, b = 8, and c = -12x = (-8 ± sqrt(8^2 - 4(-1)(-12))) / 2(-1)

= (-8 ± sqrt(64 - 48)) / (-2)

= (-8 ± 4) / (-2)

= 2, 6

Therefore, the solutions of the system of equations are x = 2 and x = 6.To interpret these solutions, we can substitute them into the original equations f(x) and g(x) to find the corresponding values of y:

f(2) = -(2)^2 + 2(2) + 4 = 2

g(2) = -(2) + 4 = 2

Therefore, the solution (2, 2) satisfies both equations f(x) and g(x).

f(6) = -(6)^2 + 2(6) + 4 = -16

g(6) = -(6) + 4 = -2

Therefore, the solution (6, -2) satisfies both equations f(x) and g(x).

So, the solutions (2, 2) and (6, -2) are the two possible solutions of the system of equations. Geometrically, they represent the points of intersection between the parabola f(x) and the straight line g(x) on the x-y plane.

User Hoziefa Alhassan
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