Answer:
x² + y² = 2
Step-by-step explanation:
Given
x + 2y = 3 → (1)
2x + y = 3 → (2)
Rearrange (2) expressing y in terms of x by subtracting 2x from both sides
y = 3 - 2x → (3)
Substitute y = 3 - 2x into (1)
x + 2(3 - 2x) = 3 ← distribute and simplify left side
x + 6 - 4x = 3
- 3x + 6 = 3 ( subtract 6 from both sides )
- 3x = - 3 ( divide both sides by - 3 )
x = 1
Substitute x = 1 into (3) and evaluate for y
y = 3 - 2(1) = 3 - 2 = 1
Thus
x² + y² = 1² + 1² = 1 + 1 = 2
