Question

What are the solutions to the system of equations? y=− x 2 +5x+6 −6x+y=6

(0,−1) and (6, 0)
(−1, 0) and (0, 6)
(0, 6) and (1, 2)
(−1, 0) and (6, 0)

Answer 1

(−1, 0) and (0, 6)

Explanation:

The given system of equations is

`y=-x^2+5x+6`

and

`-6x+y=6`

Solve for y in this second equation

`y=6x+6`

We equate the two equations to get;

`-x^2+5x+6=6x+6`

`x^2+x=0`

`x(x+1)=0`

x=0,x=-1

When x=0,

y=6(0)+6

y=6

When x=-1

y=6(-1)+6

y=0

Answer 2

option B

(−1, 0) and (0, 6)

Explanation:

Given in the question two equations,

Equation 1

y =−x² + 5x + 6

Equation 2

−6x + y = 6

plug value of y in second equation

−6x −x² + 5x + 6 = 6

-x² -6x + 5x +6 - 6 = 0

-x² - x + 0 = 0

-x² -x = 0

-x(x+1) = 0

x = 0

and

x = -1

plug value of x in second equation to find y

x = 0

−6(0) + y = 6

0 + y = 6

y = 6

and

x = -1

−6(-1) + y = 6

6 + y = 6

y = 0