Answer:
see explanation
Step-by-step explanation:
given the 2 equations
x² + y² = 34 → (1)
x + 3y = 18 → (2)
rearrange (2) by subtracting 3y from both sides
x = 18 - 3y → (3)
Substitute x = 18 - 3y into (1)
(18 - 3y)² + y² = 34
324 - 108y + 9y² + y² = 34
10y² - 108y + 324 = 34 ( subtract 34 from both sides )
10y² - 108y + 290 = 0 ← in standard form
divide through by 2
5y² - 54y + 145 = 0
(5y - 29)(y - 5) = 0 ← in factored form
Equate each factor to zero and solve for y
y - 5 = 0 ⇒ y = 5
5y - 29 = 0 ⇒ y = [tex]\frac{29}{5}[/tex]
Substitute these values into (3) for corresponding values of x
y = 5 : x = 18 - 15 = 3 ⇒ (3, 5) ← is a solution
y = [tex]\frac{29}{5}[/tex] : x = 18 - [tex]\frac{87}{5}[/tex] = [tex]\frac{3}{5}[/tex]
⇒ ( [tex]\frac{3}{5}[/tex], [tex]\frac{29}{5}[/tex] ) ← is a solution
