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Graph the system of equations. f(x)=−x^2+2x+4g(x)=−x+4 Which statements are true about the solutions to the system of equations? Select each correct answer.

An ordered pair that is the solution to the system of equations lies in Quadrant I .

An ordered pair that is the solution to the system of equations lies in Quadrant III .
An ordered pair that is the solution to the system of equations lies on the y-axis.

The x-coordinate of a solution to the system of equation is 3.

The y-coordinate of a solution to the system of equations is 4.

The y-coordinate of a solution to the system of equations is 0.

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kudzordzifrancis

ANSWER

An ordered pair that is the solution to the system of equations lies on the y-axis.

The y-coordinate of a solution to the system of equations is 4.

EXPLANATION

The given system has equations:

[tex]y = {x}^{2} + 2x + 4[/tex]

[tex]y = - x + 4[/tex]

We equate both equations to get:

[tex] {x}^{2} + 2x + 4 = - x + 4[/tex]

This implies that,

[tex] {x}^{2} + 2x + x + 4 - 4 = 0[/tex]

[tex] {x}^{2} + 3x = 0[/tex]

[tex]x(x + 3) = 0[/tex]

[tex]x = 0 \: or \: x = - 3[/tex]

When x=0, y=-(0)+4=4

When x=-3, y=-(-3)+4=7

The solutions are: (0,4) and (-3,7)

MrRoyal

The true statements about the system of equations are:

  1. (a) An ordered pair that is the solution to the system of equations lies in Quadrant I .
  2. (c) An ordered pair that is the solution to the system of equations lies on the y-axis.
  3. (d) The x-coordinate of a solution to the system of equation is 3.
  4. (e) The y-coordinate of a solution to the system of equations is 4.

The system of equations is given as:

f(x)=−x^2+2x+4

g(x)=−x+4

From the graph of the system of equations (see attachment), we have the following point of intersections

(x,y) = (0,4) and (3,1)

So, the true statements about the system of equations are:

(a), (c), (d) and (e)

Read more about system of equations at:

https://brainly.com/question/14323743

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