the equations below represent the numbers y of tickets sold after x weeks for two different local music festivals
y
10x + 150
country music festival
y
20x + 115
pop music festival
after how much time have the same number of tickets been sold for both festivals?
what is the number of tickets sold at that time?

Assuming you mean y=10x+150 and y=20x+115, you need to use a simultaneous equation, because you have two equations with two unknowns (x and y)

rearrange so
10x-y=-150
20x-y=-115

multiply the top by -1, so that if we add the two lines together, the y will cancel out
-10x+y=150
20x-y=-115

add the two lines together
10x=35
x=3.5

so the time is 3 and a half weeks

then we can sub in x to find y
20x-y=-115
20(3.5)-y=-115
70-y=-115
-y=-185
y=185

so 185 tickets were sold !
you can sub these values into your original equations to check your answer :)

(1/x + 1)^2 + 6 (1/x + 1) +5