Answer:
(5, 3 ) and (- [tex]\frac{3}{2}[/tex], - 10 )
Step-by-step 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 = - [tex]\frac{3}{2}[/tex]
Substitute these values into (3) for corresponding values of y
x = 5 : y = 2(5) - 7 = 10 - 7 = 3 ⇒ (5, 3 )
x = - [tex]\frac{3}{2}[/tex] : y = 2(- [tex]\frac{3}{2}[/tex] ) - 7 = - 3 - 7 = - 10 ⇒ (- [tex]\frac{3}{2}[/tex], - 10 )
