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CAN ANYONE PLS HELP ME I'VE BEEN STUCK ON THIS FOREVER AND WENT ON PEER ANSWER QUESTIONCOVE AND NOW BRAINLY

What are the solutions of the system?


{y=6x+6
y=−x^2+5x+6

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

Respuesta :

jcherry99
Comment
There are 3 ways you could solve this
1. You could graph it.
2. You could equate the line to the quadratic
3. You could just put the x value of the points into both equations until you get the same y value. It sometimes is the only way to solve a multiple choice math question.  I do the first two ways.

Step One
Graph the two equations.

The graph is below. 

Step 2
From the graph determine the answers.
There are two points where the graphs coincide
Check out D

Step 3
Equate the two equations. The y values must be the same.
6x + 6 = -x^2 + 5x + 6 

Step 4
Solve

6x + 6 = - x^2 + 5x + 6 The 6s cancel which is very handy.
6x = -x^2 + 5x  Pull the 2 terms on the left over to the right.
6x - 5x =  -x^2
x = - x^2   
x^2 + x = -x^2 + x^2
x^2 + x =  0      Factor
x(x + 1) = 0 

That means that 
x = 0
or 
x + 1 = 0 
x = - 1

Step 3
Find the ys
y = 6x + 6
if x = -1 
y = 6(-1) + 6
y = -6 + 6
y = 0

One of the answers is
(-1,0) <<<<<<<< Answer

Now for the other one
y = 6x + 6
x = 0
y = 6(0) + 6
y = 6

The other point is (0,6) answer <<<<<<<

D <<<<<<  Total answer 
Ver imagen jcherry99