Question

Please help:Graph the system of equations.f (x )= x^2 + x −2g (x) = −x + 1Which statements are true about the solutions to the system of equations?Select each correct answer. An ordered pair that is a solution to the system of equations lies in Quadrant III.An ordered pair that is a solution to the system of equations lies in Quadrant II.The y-coordinate of a solution to the system of equations is 4.The x-coordinate of a solution to the system of equations is −3.An ordered pair that is a solution to the system of equations lies on the x-axis.The x-coordinate of a solution to the system of equation is 2.

Answer 1

Given:

The equations given are:

$\begin{gathered} f(x)=x^2+x-2 \\ g(x)=-x+1 \end{gathered}$

Required: Identify the true statements.

Explanation:

Graph the equations.

The intersecting points (1,0) and (-3,4) are the solutions of the two equations.

The solution (-3,4) lies in the second quadrant and no solution lies in the third quadrant.

So, the statement "An ordered pair that is a solution to the system of equations lies in Quadrant III" is false and the statement "An ordered pair that is a solution to the system of equations lies in Quadrant II" is true.

The y-coordinate of the solution (-3, 4) is 4 and x-coordinate is 3. So, the statements "The y-coordinate of a solution to the system of equations is 4" and "The x-coordinate of a solution to the system of equations is −3" are true.

The solution (1,0) lies on the x-axis. Hence the statement "An ordered pair that is a solution to the system of equations lies on the x-axis" is true.

No solutions have x coordinate 2. So, the statement "The x-coordinate of a solution to the system of equation is 2" is false.

Final Answer: An ordered pair that is a solution to the system of equations lies in Quadrant II.

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

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

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