Answer:
The solutions of the system of equations are (1 , -1) and ( [tex]\frac{7}{2}[/tex] , [tex]\frac{3}{2}[/tex] )
Step-by-step explanation:
The system of equations has a quadratic equation and a linear equation to solve it equate the two equations to find the values of x and then find the values of y
∵ y = 2x² - 8x + 5 ⇒ (1)
∵ y = x - 2 ⇒ (2)
- Equate (1) and (2)
∴ 2x² - 8x + 5 = x - 2
- Subtract x from both sides
∴ 2x² - 9x + 5 = - 2
- Add 2 to both sides
∴ 2x² - 9x + 7 = 0
Let us factorize it into two factors
∵ 2x² = (2x)(x)
∵ 7 = (7)(1)
- The last sign in the trinomial is (+) and the middle sign is (-)
then the two factors have (-) middle signs
∵ (2x)(1) + (x)(7) = 2x + 7x = 9x ⇒ nears and extreams
∴ The factors of 2x² - 9x + 7 are (x - 1)and (2x - 7)
∴ (x - 1)(2x - 7) = 0
Equate each factor by 0 to find x
∵ x - 1 = 0
- Add 1 to both sides
∴ x = 1
∵ 2x - 7 = 0
- Add 7 to both sides
∴ 2x = 7
- Divide both sides by 2
∴ x = [tex]\frac{7}{2}[/tex]
Now substitute the values of x in equation (2) to find the values of y
∵ x = 1
∴ y = 1 - 2 = -1
∵ x = [tex]\frac{7}{2}[/tex]
∴ y = [tex]\frac{7}{2}[/tex] - 2 = [tex]\frac{3}{2}[/tex]
∴ The solutions of the system of equations are (1 , -1) and ( [tex]\frac{7}{2}[/tex] , [tex]\frac{3}{2}[/tex] )
