Package A contains 3 birthday cards and 2 thank you notes and costs $18. Package B contains 8 birthday cards and 6 thank you notes and costs $50. If x represents the cost of a birthday card and y represents the cost of a thank you note, how much does each birthday card cost?

Set up a system of equations.

3x + 2y = 18
8x + 6y = 50

I'm going to use the substitution method where I make one of the equations equal to the variable and then plug in to the other equation for said variable. It will make more sense as I do it. 

3x + 2y = 18
2y = - 3x + 18
Divide both sides by 2
y = - 3/2x + 9

Now our system of equations is:

y = - 3/2x + 9
8x + 6y = 50

Since there is a "y =" statement, I can plug in that first equation where the y is in the second equation. So...

8x + 6(- 3/2x + 9) = 50
8x - 9x + 54 = 50
- x + 54 = 50
Subtract 54 from both sides
- x = - 4
Divide each side by - 1
x = 4

So each birthday card is $4. To find the cost of thank you cards, we now plug in 4 where x is in either of the equations and solve for y. I'll use the first one.

3(4) + 2y = 18
12 + 2y = 18
Subtract 12 from both sides
2y = 6
Divide by 2 on both sides
y = 3

So birthday cards are $4 and thank you cards are $3.