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prohojiy [21]
3 years ago
13

the first three steps in determining the solution set of the system of equations algebraically are shown in the table. y = −x2 +

2x − 9 y = −6x + 6 What are the solutions of this system of equations? (5, −24) and (3, −12) (5, 36) and (3, 24) (−5, −24) and (−3, 12) (−5, 36) and (−3, 24)
Mathematics
2 answers:
Arlecino [84]3 years ago
6 0

Answer:

(5,-24) and  (3,-12)

Step-by-step explanation:

we have

y=-x^{2} +2x-9 -----> equation A

y=-6x+6 -----> equation B

equate the equation A and equation B

-x^{2} +2x-9=-6x+6

-x^{2} +2x-9+6x-6=0

-x^{2} +8x-15=0

The formula to solve a quadratic equation of the form ax^{2} +bx+c=0 is equal to


x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}


in this problem we have


-x^{2} +8x-15=0

so


a=-1\\b=8\\c=-15


substitute in the formula


x=\frac{-8(+/-)\sqrt{8^{2}-4(-1)(-15)}} {2(-1)}


x=\frac{-8(+/-)\sqrt{64-60}} {-2}


x=\frac{-8(+/-)2}{-2}


x=\frac{-8+2}{-2}=3


x=\frac{-8-2}{-2}=5


Find the values of y

For x=3

y=-6x+6 ------> y=-6(3)+6=-12

For x=5

y=-6x+6 ------> y=-6(5)+6=-24

The solutions are the points (3,-12) and (5,-24)

Nookie1986 [14]3 years ago
3 0
It is A! I know because i just took the test!
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