If x+2y =3 and 2x+y=3 then find x²+y²

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