Question

Please help!!

Solve linear-quadratic system algebraically. Show all work.

6x + y = –16
y + 7 = x^2

Answer 1

solution set (x,y)= (-3,2)

Step-y-step explanation:

we have

6x +y =-16------------1

y + 7 = x²----------2

solve for y

from equation 1....... y =-16-6x---------------3

from equation 2.......y= x²-7-----------------4

comparing equation 3 and 4

-16- 6x= x²-7

x²-7+16+6x=0

x²+6x+9 =0

factorize

x²+3x+3x+9 =0

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

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

(x+3)=0

x=-3

adding the vale of x in equation 4

y = x²-7

y= (-3)²-7

y=9-7=2

so solution set is (x,y)= (-3,2)

Answer 2

Answer:x = - 3 twice

Explanation:

6x + y = –16 - - - - - - 1

y + 7 = x^2 - - - - -2

From equation 1, y = - 16 - 6x

Substituting y = - 16 - 6x into equation 2, it becomes

- 16 - 6x + 7 = x^2

x^2 + 6x + 9 = 0

x^2 + 6x + 9 = 0

Solving the quadratic equation by factorization method, we will pick two numbers such that their sum is 6x and their product is 9. So we will pick 3x and 3x. It becomes

x^2 + 3x + 3x + 9 = 0

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

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

x + 3 = 0 or x + 3 =0

x = -3 or x =-3

Therefore, x = - 3 twice

Substituting x = - 3 into equation 1, it becomes

6 × -3 + y = –16

-18 + y = - 16

y = - 16 + 18

y = 2