What are the solutions to the system of equations? { Y=2x^2-6x+3 { y=x-2

Question

What are the solutions to the system of equations?
{ Y=2x^2-6x+3
{ y=x-2

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2 weeks 2021-09-10T22:28:51+00:00 2 Answers 0

see explanation

Step-by-step explanation:

Given the 2 equations

y = 2x² – 6x + 3 → (1)

y = x – 2 → (2)

Since both equations express y in terms of x we can equate the right sides, that is

2x² – 6x + 3 = x – 2 ( subtract x – 2 from both sides )

2x² – 7x + 5 = 0 ← in standard form

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 2 × 5 = 10 and sum = – 7

The factors are – 2 and – 5

Use these factors to split the x- term

2x² – 2x – 5x + 5 = 0 ( factor the first/second and third/fourth terms )

2x(x – 1) – 5(x – 1) = 0 ← factor out (x – 1) from each term

(x – 1)(2x – 5) = 0

Equate each factor to zero and solve for x

x – 1 = 0 ⇒ x = 1

2x – 5 = 0 ⇒ 2x = 5 ⇒ x =

Substitute these values into (2) for corresponding values of y

x = 1 : y = 1 – 2 = – 1 ⇒ (1, – 1)

x = : y = – 2 =

Solutions are (1, – 1) and ( , )