{x²+xy+y²=7 {y+x=3

To solve this system of equations, we can use the method of substitution. Let's solve the second equation for y:

y = 3 - x

Now substitute this value of y into the first equation:

x^2 + x(3 - x) + (3 - x)^2 = 7

Simplifying:

x^2 + 3x - x^2 + 9 - 6x + x^2 = 7

Combining like terms:

3x - 6x + 9 = 7

Simplifying further:

-3x + 9 = 7

Subtracting 9 from both sides:

-3x = -2

Dividing by -3:

x = 2/3

Now substitute this value of x back into the second equation:

y + 2/3 = 3

Subtracting 2/3 from both sides:

y = 3 - 2/3

Simplifying:

y = 7/3

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