Question

Solve the system algebraically. Enter your answer as two points of intersection. Example Answer 1: (a.b) Answer 2: (c.d)

y = x² - 10x + 14
y = 7x - 16
Answer 1:
Answer 2:

Answer 1

To solve the given system of equations algebraically, set the two equations equal to each other, rearrange the equation, factor the quadratic equation, and solve for x. The two points of intersection are (2, 0) and (15, 0).

Step-by-step explanation:

1. First, set the two equations equal to each other: x² - 10x + 14 = 7x - 16
2. Next, rearrange the equation to bring all terms to one side: x² - 17x + 30 = 0
3. Now, factor the quadratic equation: (x - 2)(x - 15) = 0
4. Set each factor equal to zero and solve for x: x - 2 = 0 or x - 15 = 0
5. Thus, the two points of intersection are (2, 0) and (15, 0).

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