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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 = = 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 !).
Solved.
On the way, you learned on how the Elimination method works.