Question

Which represents the solution(s) of the graphed system of equations, y = –x2 + x + 2 and y = –x + 3? (1, 2) (1, 2) and (0, 3) (–1, 0) and (2, 0) (2, 1)

Answer 1

y = -x^2 + x + 2
y = -x + 3

-x + 3 = -x^2 + x + 2
x^2 - x - 2 - x + 3 = 0
x^2 -2x + 1 = 0
(x - 1)(x - 1) = 0

x - 1 = 0 y = -x + 3
x = 1 y = -1 + 3
y = 2

solutions are : (1,2) , (1,2)

Answer 2

(1,2) , (1,2)

Explanation:

Given :
`y = -x^2 + x + 2`

`y = -x + 3`

To Find : Which represents the solution(s) of the graphed system of equations

Solution:

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

`y = -x + 3`

Now, to find the solution

`-x + 3 = -x^2 + x + 2`

`x^2 - x - 2 - x + 3 = 0`

`x^2 -2x + 1 = 0`

`(x - 1)(x - 1) = 0`

So,
`x = 1,1`

Substitute the value of x

`y = -x + 3`

`y = -1 + 3`
`y = 2`

Thus the solutions are : (1,2) , (1,2)