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What are the solutions to the following system of equations? y = x2 + 3x − 7 3x − y = −2 (2 points) (3, 11) and (−3, −7) (11, 3) and (−3, −7) (3, 11) and (−7, −3) No real solutions

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ANSWER

(3, 11) and (−3, −7)


EXPLANATION

The given system of equations are:


[tex]y = {x}^{2} + 3x - 7[/tex]

and

[tex]3x - y = - 2[/tex]

or

[tex]y = 3x + 2[/tex]


We equate the two equations to obtain,



[tex]{x}^{2} + 3x - 7 = 3x + 2[/tex]

We rewrite in standard quadratic form to obtain,

[tex]{x}^{2} + 3x - 3x - 7 - 2 = 0[/tex]


This simplifies to

[tex]{x}^{2}- 9= 0[/tex]


We solve for x to obtain,


[tex] {x}^{2} = 9[/tex]

[tex]x = \pm \sqrt{9} [/tex]

[tex]x = \pm 3[/tex]

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

When
[tex]x = 3[/tex]

[tex]y = 3(3) + 2 = 11[/tex]

When x=-3,

[tex]y = 3( - 3) + 2 = - 7[/tex]


Therefore the solution for the system is (3, 11) and (−3, −7).
zainebamir540

Answer:

Choice A is correct answer.

Step-by-step explanation:

We have given a system of equations.

y = x² + 3x − 7                                        eq(1)

3x − y = −2                                            eq(2)

We have to find the solution of given system of equations.

Adding -3x to both sides of eq(2), we have

-3x+3x-y = -3x-2

-y = -3x-2

y = 3x+2                          eq(3)

Now, putting the value of y in eq(1), we have

3x+2 = x²+3x-7

Adding -3x to both sides of above equation, we have

-3x+3x+2 = -3x+x²+3x-7

2 = x²-7

Adding 7 to both sides of above equation, we have

2+7 = x²-7+7

9 = x²

Taking square root to both sides of above equation, we have

√9 = √x²

±3 = x

Putting the value of x in eq(3), we have

y = 3(±3)+2

y = 3(3)+2 and y = 3(-3)+2

y = 9+2 and y = -9+2

y = 11 and y = -7

Hence, the solutions of given system are :

(3,11) and (-3,-7)