Respuesta :
Answer:
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 = [tex]\frac{5}{2}[/tex]
Substitute these values into (2) for corresponding values of y
x = 1 : y = 1 - 2 = - 1 ⇒ (1, - 1)
x = [tex]\frac{5}{2}[/tex] : y = [tex]\frac{5}{2}[/tex] - 2 = [tex]\frac{1}{2}[/tex]
Solutions are (1, - 1) and ( [tex]\frac{5}{2}[/tex], [tex]\frac{1}{2}[/tex] )
