Question

Solve the system of equations using substitution or graphing.

Answer 1

Explanation:

I think substitution would be the easiest since you already have one of the variables solved for.

`y=-x^2+4x+5\\y=x+1\\x+1=-x^2+4x+5\\x^2-3x-4=0\\(x-4)(x+1)=0\\x-4=0\\x=4\\x+1=0\\x=-1`

(You can just set the equations equal to each other since they both equal y).

Now, to get the points, plug in x = 4 and x = -1 into one of the equations (I'm going to plug them into y = x+1 because that one is much simpler)

`y(4)=4+1\\y(4)=5\\y(-1)=-1+1\\y(-1)=0`

So, your final points are:

(4,5) and (-1,0)

Answer 2

Answer: A

Explanation:

We can use substitution to solve this problem. Since we are given y=-x²+4x+5 and y=x+1, we can set them equal to each other.

-x²+4x+5=x+1 [subtract both sides by x]

-x²+3x+5=1 [subtract both sides by 1]

-x²+3x+4=0

Now that we have the equation above, we can factor it to find the roots.

-x²+3x+4=0 [factor out -1]

-1(x²-3x-4)=0 [factor x²-3x-4]

-1(x+1)(x-4)=0

This tells us that x=-1 and x=4.

We can narrow down our answer to A, but let's plug in those values to be sure it is correct.

-(-1)²+4(-1)+5=(-1)+1 [exponent]

-1+4(-1)+5=-1+1 [multiply]

-1-4+5=-1+1 [add and subtract from left to right]

0=0

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-(4)²+4(4)+5=(4)+1 [exponent]

-16+4(4)+5=4+1 [multiply]

-16+16+5=4+1 [add and subtract from left to right]

5=5

Therefore, we can conclude that A is the correct answer.