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JasonZhu
In order to utilize the graph, first you have to distinguish which graph accurately pertains to the two functions.

This can be done by rewriting the equations in the form y = mx + b which can be graphed with ease; where m is the slope and b is the y intercept.

-x^2 + y = 1
y = x^2 + 1

So this will be a basic y = x^2 parabola where the center intercepts on the y axis at (0, 1)

-x + y = 2
y = x +2

So this will be a basic y = x linear where the y intercept is on the y axis at (0, 2)

The choice which depicts these two graphs correctly is the first choice. The method to find the solutions to the system of equations by using the graph is by determining the x coordinate of the points where the two graphed equations intersect.

The points ( 1.16,  3.16 ),( -0.61,  1.39 ).

Intersection of point

It can be determined when two graphs intersect each other.

How to get an intersection point?

[tex]y = x^{2} + 1\\y = x + 2[/tex]

From both equation

[tex]\begin{aligned} x^{2} + 1 = x + 2\\x^{2} -x-1 =0 \\(x-1.16)(x+0.61) = 0\\x = 1.16,-0.61\\\end{aligned}[/tex]

For x = 1.16 then y = 3.16

For x = -0.61 then y = 1.39

So the points ( 1.16,  3.16 ),( -0.61,  1.39 )

Thus, the points ( 1.16,  3.16 ),( -0.61,  1.39 ).

More about the Intersection of point link is given below.

https://brainly.com/question/12089275

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