10.4k views
2 votes
How many solutions does the system have? {y=−3x+5y=x^2−3x+5 Enter your answer in the box

User CAD
by
8.7k points

2 Answers

6 votes

Answer:

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

User Tiffiny
by
8.6k points
3 votes
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).
User Minimalpop
by
8.0k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories