Simulatenous equations (Quadratic + linear)

If (2,1) is a solution fo the simultaneous equations,

x^2 + xy + ay = b

2ax + 3y = b

A) Find the value of a and of b. [a=1, b =7]

B) Find also the other solution [x=-7 and y = 7)

I have solved both parts, but I face a problem.

After part a), I substituted values of a and b into the equation to obtain

x^2 + xy + y = 7 and 2x + 3y = 7

Substituting x = (7-3y)/2 into the equation x^2 + xy + y = 7

I obtain the quadratic expression y^2 - 9y + 14 = 0

Hence, I get y = 7 and y =2 ; x = -7 and x = 1/2

Why do I reject y =2 and x = 1/2 combination ?

I know that substituting the above into 2x + 3y = 7 satisfies the equation

But it doesn't satisfy x^2 + xy + y = 7. How would I know?

Thanks