Function or not

Question

Substitute -6 for x in each equation and solve for y. Use your results to explain why y=x^2-5x is a function and x=y^2-5y is not.

I need help solving x=y^2-5y.

Answer 1

When you substitute x = -6 in the first equation you get the single value 36.

 

When you do the same thing for the 2nd equation you get: -6 = y² - 5y, which is a quadratic equation in y which has 2 solutions, namely, y = 3 and y = 2, i.e. a single value of x gives 2 values of y...which means he second equatoin is NOT a function.

 

You should graph the second equation to see what the above answer means!