Solve the simultaneous equations
x-6y=5
xy - 2y2 = 6
-
Show clear algebraic working.

(- 7, - 2 ) , (9.5, 0.75 )

Step-by-step explanation:

Given the equations

x - 6y = 5 ( add 6y to both sides )

x = 5 + 6y → (1)

xy - 2y² = 6 → (2)

Substitute x = 5 + 6y into (2)

(5 + 6y)y - 2y² = 6 ← distribute and rearrange left side

5y + 6y² - 2y² = 6

4y² + 5y = 6 ( subtract 6 from both sides )

4y² + 5y - 6 = 0 ← in standard form

(y + 2)(4y - 3) = 0 ← in factored form

Equate each factor to zero and solve for y

y + 2 = 0 ⇒ y = - 2

4y - 3 = 0 ⇒ 4y = 3 ⇒ y = = 0.75

Substitute these values into (1) for corresponding values of x

y = - 2 : x = 5 + 6(- 2) = 5 - 12 = - 7 ⇒ (- 7, - 2 )

y = 0.75 : x = 5 + 6(0.75) = 5 + 4.5 = 9.5 ⇒ (9.5, 0.75 )