Answer:
see explanation
Step-by-step explanation:
Given the 2 equations
y - 3 = 2x → (1)
20 + xy = 5y → (2)
Rearrange (1) expressing y in terms of x by adding 3 to both sides
y = 2x + 3 → (3)
Substitute y = 2x + 3 into (2)
20 + x(2x + 3) = 5(2x + 3) ← distribute parenthesis
20 + 2x² + 3x = 10x + 15 ← subtract 10x + 15 from both sides
2x² - 7x + 5 = 0 ← in standard form
(x - 1)(2x - 5) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 1 = 0 ⇒ x = 1
2x - 5 = 0 ⇒ 2x = 5 ⇒ x = [tex]\frac{5}{2}[/tex]
Substitute each of these values into (3) for corresponding values of y
x = 1 : y = 2 + 3 = 5 ⇒ P(1, 5 )
x = [tex]\frac{5}{2}[/tex] : y = 5 + 3 = 8 ⇒ Q([tex]\frac{5}{2}[/tex], 8 )
