{x²+xy+y²=7 y+x=3

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

Let's solve it using substitution method:

We have the second equation as y + x = 3. We can solve it for y by subtracting x from both sides: y = 3 - x

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

Expanding the equation, we get: x² + 3x - x² + 9 - 6x + x² = 7

Simplifying, we have: 3x - 6x + 9 = 7

Combining like terms, we get: -3x + 9 = 7 -3x = 7 - 9 -3x = -2

Dividing both sides by -3, we finally obtain: x = 2/3

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

Subtracting 2/3 from both sides, we have: y = 3 - 2/3 = 9/3 - 2/3 = 7/3

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