Respuesta :

Answer:

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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ANSWER

One solution,

(0,5)

EXPLANATION

The given expression:

[tex]y = - 3x + 5[/tex]

and

[tex]y = {x}^{2} - 3x + 5[/tex]

We equate the two equations to get,

[tex]{x}^{2} - 3x + 5 = - 3x + 5[/tex]

This implies that,

[tex]{x}^{2} - 3x + 3x + 5 - 5 = 0[/tex]

[tex] {x}^{2} = 0[/tex]

[tex]x = 0[/tex]

We put this value of x into any of the equations to get,

[tex]y = - 3(0) + 5[/tex]

[tex]y = 5[/tex]

The system has only one solution,

(0,5).

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