Question

Solve algebraically
x2 + y2 = 18
x-2y=-3

Answer 1

(-
`(3)/(5)`, -
`(21)/(5)` ) and (3, 3 )

Explanation:

Given the 2 equations

x² + y² = 18 → (1)

x - 2y = - 3 → (2)

Rearrange (2) expressing x in terms of y by adding 2y to both sides.

x = 2y - 3 → (3)

Substitute x = 2y - 3 into (1)

(2y - 3)² + y² = 18 ← expand left side and simplify

4y² - 12y + 9 + y² = 18

5y² - 12y + 9 = 18 ( subtract 18 from both sides )

5y² - 12y - 9 = 0 ← in standard form

(5y + 3)(y - 3) = 0 ← in factored form

Equate each factor to zero and solve for y

5y + 3 = 0 ⇒ 5y = - 3 ⇒ y = -
`(3)/(5)`

y - 3 = 0 ⇒ y = 3

Substitute these values into (3) for corresponding values of x

y = -
`(3)/(5)` : x = -
`(6)/(5)` - 3 = -
`(21)/(5)` ⇒ ( -
`(3)/(5)`, -
`(21)/(5)` )

y = 3 : x = 6 - 3 = 3 ⇒ (3, 3 )