When designing an experiment, why is it important to test only one variable?

That's the only way you can get consistent and accurate results. 

I will try to explain more in depth. Lets say Jimmy frequently has headaches and needs medicine to treat it. Jimmy uses Headfix and Achefix both in one experiment. The next day, Jimmy feels great. His headaches are cured, but since Jimmy used 2 variables (the 2 medicines), he is left with three options

a. Headfix worked
b. Achefix worked
c. Both worked.

Now Jimmy has no idea what solved his problem. It could be 3 possible answers. However, if he used one variable at a time and had two experiments instead, lets see what happens.

Jimmy uses Headfix.
a. It worked
b. It didn't work

Headfix did not work.

Next experiment Jimmy uses Achefix
a. It worked
b. It didn't work

Achefix worked.

Now instead of having three possible solutions, you have 1 definite answer experiment. Therefore you cannot use more than one variable because there could be multiple outcomes and you do not know which variable affected the results differently/

Ibelieve the correct answer would be c.

That big glowy thing in the sky is called the sun