Question

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.

Answer 1

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:

$y = {x}^{2} + 2x + 4$

$y = - x + 4$

We equate both equations to get:

${x}^{2} + 2x + 4 = - x + 4$

This implies that,

${x}^{2} + 2x + x + 4 - 4 = 0$

${x}^{2} + 3x = 0$

$x(x + 3) = 0$

$x = 0 \: or \: x = - 3$

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

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

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