Question

Solve the simultaneous equations
3
2x - y = 7
xy = 15

Answer 1

(5, 3 ) and (-
`(3)/(2)`, - 10 )

Explanation:

Given the 2 equations

2x - y = 7 → (1)

xy = 15 → (2)

Rearrange (1) expressing y in terms of x , that is

y = 2x - 7 → (3)

Substitute y = 2x - 7 into (2)

x(2x - 7) = 15

2x² - 7x = 15 ( subtract 15 from both sides )

2x² - 7x - 15 = 0 ← in standard form

(x - 5)(2x + 3) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 5 = 0 ⇒ x = 5

2x + 3 = 0 ⇒ 2x = - 3 ⇒ x = -
`(3)/(2)`

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

x = 5 : y = 2(5) - 7 = 10 - 7 = 3 ⇒ (5, 3 )

x = -
`(3)/(2)` : y = 2(-
`(3)/(2)` ) - 7 = - 3 - 7 = - 10 ⇒ (-
`(3)/(2)`, - 10 )