{x²+xy+y²=7 {y+x=3

To solve this system of equations, we can use the substitution method.

First, we'll solve the second equation, y+x=3, for y: y = 3-x

Now, substitute this value of y in the first equation: x² + x(3-x) + (3-x)² = 7

Simplify the equation: x² + 3x - x² + 9 - 6x + x² = 7

Combine like terms: 3x - 6x + 9 = 7

Simplify: -3x + 9 = 7

Subtract 9 from both sides: -3x = -2

Divide by -3: x = 2/3

Now, substitute this value of x back into the second equation to find y: y + (2/3) = 3

Subtract (2/3) from both sides: y = 3 - (2/3) y = 7/3

Therefore, the solution to the system of equations is x = 2/3 and y = 7/3.