SOLUTION: 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 birt

From the condition, you have this system of 2 equations in two unknowns

3x + 2y = 18,    (1)
8x + 6y = 50.    (2)


Multiply eq(1) by 3 (both sides).  Keep the equation (2) as is. You have

9x + 6y = 54,    (1')
8x + 6y = 50.    (2')


Now subtract eq(2') from eq(1').  The terms "6y" will cancel each other, and you will get a single equation for only one unknown x:

    (It is how the Elimination method works).


9x - 8x = 54 - 50  ====>  x = 4.


Thus we just found that one birthday card costs 4 dollars.


Then from eq(1)  

3*4 + 2y = 18  ====>  2y = 18 - 12 = 6  ====>  y =  = 3.


Answer.  One birthday card costs 4 dollars.  One "thank you note"  costs 3 dollars.

Check.   Please check the solution on your own.  (It is a necessary part of the solution !).