One gym charges a $50 sign up fee and $65 per month. another gun charges a $90 sign up fee and $45 per month. foe what number of months is the cost of the gyms equal?

2 months.
the equations are
65m+50 and 45m+90
you set them equal together
65m+50=45m+90 
and you get 2.

Y=65x+50
y=45x+90
Just put them equal to each other
65x+59=45x+90
Then solve you will get x=2 finally check plug 2 in for both equations and the will be equal
You will get 180 for both after you plug in