solve, explaining steps --thank you in advance

Question

Miranda bought 1 snack and 6 movie tickets and spent $13. Jared bought 3 snacks and 2 movie tickets and spent $7. What is the cost for one snack and one movie ticket?

Define variables:

X =

Y =

Write two equations:

Solve using substitution or elimination.

answer in context

Answer 1

If you let X represent the price of a snack and Y the price of a movie ticket, then Miranda spent $13 on 1 X and 6 Y, thus 13 = X + 6Y. Likewise, by Jared's purchases, 3X + 2Y = 7

Since 13 = X + 6Y, by subtracting 6Y from both sides, this becomes 13 - 6Y = X

3X + 2Y = 7 and by substituting, this becomes 3(13 - 6Y) + 2Y = 7

Multiplying out gives 39 - 18Y + 2Y = 39 - 16Y = 7

By adding 16Y to both sides and subtracting 7 from both sides, this becomes 32 = 16Y

By dividing both sides by 16, this becomes 2 = Y

Since X + 6Y = 13, then X + (6*2) = 13 -> X + 12 = 13 -> X = 1

Now all I want to know is where the heck is this movie theater with such cheap prices?