Answer:
(-2, 11) and (2, 3)
Step-by-step explanation:
Given system of equations:
1) f(x) = x² - 2x + 3 ⇒ y = x² - 2x + 3
2) f(x) = -2x + 7 ⇒ y = -2x + 7
Solve Using the Substitution Method:
Step 1: Substitute the the first equation into the second.
⇒ x² - 2x + 3 = -2x + 7
Step 2: Solve for x.
x² - 2x + 3 = -2x + 7 [ Add 2x to both sides. ]
x² - 2x + 2x + 3 = -2x + 2x + 7
⇒ x² + 3 = 7 [ Subtract 3 from both sides. ]
x² + 3 - 3 = 7 - 3
⇒ x² = 4 [ Take the square root of both sides. ]
√x² = √4
x = ± 2
⇒ x = -2, x = 2
Step 3: Solve for y.
Substitute the found x-values into one of the given equations.
y = -2x + 7 ⇒ y = -2(-2) + 7 ⇒ y = 4 + 7 ⇒ y = 11
y = -2x + 7 ⇒ y = -2(2) + 7 ⇒ y = -4 + 7 ⇒ y = 3
The solutions to the system of equations are: (-2, 11) and (2, 3).
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