How do you solve y=-x^2-6x-3, y=6y=−x2−6x−3,y=6 using substitution?

2 Answers
EET-AP
Feb 17, 2017

x = -3x=−3; y = 6y=6

Explanation:

y = 6y=6 is given in the question, but it still is part of the answer.

To solve for xx, substitute y = 6y=6 into the equation:

y = -x^2 -6x -3y=−x2−6x−3

6 = -x^2 -6x -36=−x2−6x−3

Multiply both sides by -1−1

-6 = x^2 +6x +3−6=x2+6x+3

Add 6 to both sides:

0 = x^2 +6x +90=x2+6x+9

Factor the equation by calculating factors of the first and last numbers that will add or subtract to arrive at the inner number.

0 = (x + 3) (x + 3 )0=(x+3)(x+3)

In this case both factors will provide the same answer for xx:

0 = (x + 3)0=(x+3)

-3 = x−3=x

To check, substitute x and yxandy into the equation:

y = -x^2 -6x -3y=−x2−6x−3

6 = -(-3)^2 -6(-3) -36=−(−3)2−6(−3)−3

6 = -9 +18 -36=−9+18−3

6 = -12 +18 = 66=−12+18=6

Barney V.
Feb 17, 2017

x=-3x=−3

Explanation:

y=-x^2-6x-3y=−x2−6x−3 given y=6y=6

substitute y=6y=6

:.-x^2-6x-3=6

multiply both sides by -1

:.x^2+6x+3=-6

:.x^2+6x+3+6=0

:.x^2+6x+9=0

:.(x+3)(x+3)=0

:.x+3=0

:.x=-3

Check:

substitute y=6,x=-3

:.6=-(-3)^2-6(-3)-3

:.6=-9+18-3

:.6=-9+15

:.6=6

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