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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)

Respuesta :

texaschic101
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:

(1,2) , (1,2)

Step-by-step explanation:

Given : [tex]y = -x^2 + x + 2[/tex]

            [tex]y = -x + 3[/tex]

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

Solution:

[tex]y = -x^2 + x + 2[/tex]

[tex]y = -x + 3[/tex]

Now, to find the solution

[tex]-x + 3 = -x^2 + x + 2[/tex]

[tex]x^2 - x - 2 - x + 3 = 0[/tex]

[tex]x^2 -2x + 1 = 0[/tex]

[tex](x - 1)(x - 1) = 0[/tex]

So, [tex]x = 1,1[/tex]

Substitute the value of x

[tex]y = -x + 3[/tex]

[tex]y = -1 + 3[/tex][tex]y = 2[/tex]

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

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