Respuesta :

Answer:

the graph is attached below :

Step-by-step explanation:

To make the graph which represent the solution set of the given equations :

First draw the graphs of both the given equations then the the point of intersection of both the graphs is the solution of the given equations.

Now, the given equations are :

y = x² - 4 and x + y + 2 = 0

Now the first equation is quadratic and of the parabola.

And the second equation is of a straight line.

Now. as the first equation is quadratic so the solution set of both the equations will contain two points.

Hence, the equations will have two solutions and the required graph of the solution set is attached below :

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The point of intersection of given equation is (-2,0) and (1,-3). The graph which represent the solution of the given set of equation is attached below.

What is system of equation?

A system of equation is the set of equation in which the finite set of equation is present for which the common solution is sought.

Given information-

The equations given in the problem are,

[tex]y = x^2 - 4[/tex]

[tex]x+y+2=0[/tex]

The first equation of given in the problem is equation of parabola, which is,

[tex]y = x^2 - 4[/tex]

Let the above equation as equation 1.

The second equation of given in the problem is equation of straight line, which is,

[tex]x+y+2=0[/tex]

Put the value of y from equation 1 as,

[tex]x+x^2-4+2=0\\x^2+x-2=0\\x^2+2x-x-2=0\\x(x+2)-1(x+2)=0\\(x+2)(x-1)=0\\x=-2,1[/tex]

Put this value in equation one as,

For -2 value,

[tex]y = (-2)^2 - 4\\y=0[/tex]

For 1 value,

[tex]y = (1)^2 - 4\\y=-3[/tex]

Thus the point of intersection of given equation is (-2,0) and (1,-3). The graph which represent the solution of the given set of equation is attached below.

Learn more about the system of equations here;

https://brainly.com/question/13729904

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