Answer:
(- [tex]\frac{3}{5}[/tex], - [tex]\frac{21}{5}[/tex] ) and (3, 3 )
Step-by-step 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 = - [tex]\frac{3}{5}[/tex]
y - 3 = 0 ⇒ y = 3
Substitute these values into (3) for corresponding values of x
y = - [tex]\frac{3}{5}[/tex] : x = - [tex]\frac{6}{5}[/tex] - 3 = - [tex]\frac{21}{5}[/tex] ⇒ ( - [tex]\frac{3}{5}[/tex], - [tex]\frac{21}{5}[/tex] )
y = 3 : x = 6 - 3 = 3 ⇒ (3, 3 )
