What are the solutions to the system of equations?

Ответ:

michaelowenmccollum

12.03.2022

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 = $\frac{5}{2}$

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

x = 1 : y = 1 - 2 = - 1 ⇒ (1, - 1)

x = $\frac{5}{2}$ : y = $\frac{5}{2}$ - 2 = $\frac{1}{2}$

Solutions are (1, - 1) and ( $\frac{5}{2}$ , $\frac{1}{2}$ )

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