Question

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

Answer 1

There are 2 solutions

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

Answer 2

ANSWER

One solution,

(0,5)

EXPLANATION

The given expression:


`y = - 3x + 5`

and


`y = {x}^(2) - 3x + 5`

We equate the two equations to get,


`{x}^(2) - 3x + 5 = - 3x + 5`

This implies that,


`{x}^(2) - 3x + 3x + 5 - 5 = 0`


`{x}^(2) = 0`


`x = 0`

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


`y = - 3(0) + 5`


`y = 5`

The system has only one solution,

(0,5).