SOLUTION: Given that 3x + 2y = 5a + b and 4x - 3y = a + 7b, solve for x in terms of a and b.

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Question 1136284: Given that 3x + 2y = 5a + b and 4x - 3y = a + 7b, solve for x in terms of a and b.
Answer by ikleyn(52777) About Me  (Show Source):
You can put this solution on YOUR website!
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3x + 2y = 5a +  b     (1)

4x - 3y =  a + 7b     (2)


I think that the shortest (the most straightforward) way to get the goal is to eliminate "y".
For it, multiply eq(1) by 3 (both sides) and multiply eq(2) by 2. You will get


9x + 6y = 15a + 3b     (3)

8x - 6y =  2a + 14b    (4)



Now add eq(4) and eq(3).  You will get 



17x = 17a + 17b   ========>  x = a + b.      ANSWER

Solved.