Answer:
see explanation
Step-by-step explanation:
Given the 2 equations
x² + y² = 5 → (1)
2x + y = 4 → (2)
Rearrange (2) expressing y in terms of x by subtracting 2x from both sides
y = 4 - 2x → (3)
Substitute y = 4 - 2x in (1)
x² + (4 - 2x)² = 5 ← expand factor on left side
x² + 16 - 16x + 4x² = 5
5x² - 16x + 16 = 5 ( subtract 5 from both sides )
5x² - 16x + 11 = 0 ← in standard form
(5x - 11)(x - 1) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 1 = 0 ⇒ x = 1
5x - 11 = 0 ⇒ 5x = 11 ⇒ x = [tex]\frac{11}{5}[/tex]
Substitute each of these values into (3) for corresponding values of y
x = 1 : y = 4 - 2 = 2 ⇒ P(1, 2)
x = [tex]\frac{11}{5}[/tex] : y = 4 - [tex]\frac{22}{5}[/tex] = - [tex]\frac{2}{5}[/tex]
Hence Q( [tex]\frac{11}{5}[/tex], -[tex]\frac{2}{5}[/tex] )
