Question

What are the solutions to the system of equations?

{y=2x2−8x+5
{y=x−2

Answer 1

The solutions of the system of equations are (1 , -1) and (
`(7)/(2)` ,
`(3)/(2)` )

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 =
`(7)/(2)`

Now substitute the values of x in equation (2) to find the values of y

∵ x = 1

∴ y = 1 - 2 = -1

∵ x =
`(7)/(2)`

∴ y =
`(7)/(2)` - 2 =
`(3)/(2)`

∴ The solutions of the system of equations are (1 , -1) and (
`(7)/(2)` ,
`(3)/(2)` )