How many solutions does the system have? {y=−3x+5y=x^2−3x+5 enter your answer in the box

There are 2 solutions

Step-by-step explanation:

Given the 2 equations

y = 3x + 5 → (1)

y = x² - 3x + 5 → (2)

Substitute y = x² - 3x + 5 into (1)

x² - 3x + 5 = 3x + 5 ← Subtract 3x + 5 from both sides

x² - 6x = 0 ← factor out x from each term

x(x - 6) = 0

Equate each factor to zero and solve for x

x = 0

x - 6 = 0 ⇒ x = 6

Substitute these values into (1) for corresponding values of y

x = 0 : y = 0 + 5 = 5 ⇒ (0, 5) ← is a solution

x = 6 : y = (3 × 6) + 5 = 18 + 5 = 23 ⇒ (6, 23) ← is a solution

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step-by-step explanation:

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step-by-step explanation:

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