You can put this solution on YOUR website! Consider two equations
a1x+b1y+c1=0 a1 ,b1,a2,b2 not equal to 0
a2x+b2y+c2=0
For a unique solution
a1/b1 not equal to a2/b2
For innumerable solutions
a1/a2 =b1/b2=c1/c2
For no solution
a1/a2 = b1/b2 not equal to c1/c2
The response from the other tutor has nothing to do with the question that is asked.
Her response is about PAIRS of equations which have no COMMON SOLUTION. The question is about single polynomial equations that have no REAL ROOTS.
A polynomial equation of odd degree will always have at least one real solution, because the end behavior for large positive x is different than for large negative x.
A polynomial equation of even degree does not need to have a real root, because the end behavior for large positive x and for large negative x is the same. If a polynomial equation of even degree has all coefficients positive, then every term will be positive and the equation will have no real solutions; and likewise if all terms have negative coefficients.
Here are graphs of two polynomial equations with no real solutions:
