Question 1108815
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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 = {{{6/2}}} = 3.


<U>Answer</U>.  One birthday card costs 4 dollars.  One "thank you note"  costs 3 dollars.

<U>Check</U>.   Please check the solution on your own.  (It is a <U>necessary part</U> of the solution !).
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Solved.


On the way, you learned on how the Elimination method works.