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What is the solution set of this system of equations?
y = x2 − 3x − 4
x = y + 8

a.{(-1, 0), (4, 0)}
b.{(8, 0), (0, 8)}
c.{(0, 0)}
d.{(2, -6)}
e.There is no real solution.

Please help me, I'm afraid I will fail. Please no "solve it yourself" answers. Thank you guys so much! <3

Respuesta :

GHulamMUhammad
d option is right answer

Answer:

Option: d is the correct answer.

The solution set of this system of equations is:

             d.   {(2, -6)}

Step-by-step explanation:

We are given a system if equations by:

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

and  [tex]x=y+8[/tex]

i.e. [tex]y=x-8-------(2)/tex]

Hence, we will put the value of y from equation (2) in equation (1)

[tex]x-8=x^2-3x-4\\\\\\i.e.\\\\\\x^2-3x-x-4+8=0\\\\\\i.e.\\\\\\x^2-4x+4=0\\\\\\i.e.\\\\\\(x-2)^2=0\\\\i.e.\\\\\\x=2[/tex]

Also, from equation (2) we get:

[tex]y=2-8\\\\\\i.e.\\\\\\y=-6[/tex]

Hence, the solution set is:  {(2,-6)}

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