Question

G

Which represents the solution(s) of the graphed system of equations, y = -x² + x + 2 and y = -x + 3
5
4
3
2
←+
-5-4-3-2-1,
2 3 4 5
O (1, 2)
Next
Mark this and return
-2+
8 + 9
(1 21 and 10 21
X
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Answer 1

Answer: (1, 2)

Explanation:

y = -x² + x + 2

y = -x + 3

1. Set the two equations equal to each other:

-x² + x + 2 = -x + 3

2. move one of the equations to the other side:

-x² + 2x - 1

3. Factor out a -1:

-1 (-x² + 2x - 1) = 0

x² - 2x + 1

4. Factor:

(x - 1)(x - 1)

x = 1

5. Plug in 1 to one of the equations:

y = -x + 3

y = -(1) + 3

y = 2

6. Write as coordinates:

(1, 2)