Answer to Question 3

Remember:  In mathematics there are often many acceptable solutions to a problem.  These answers show you "possible" solutions.  While the answers are always the same, the methods of arriving at the answers may differ.

3.

If the "a" and "b" in this problem bother you, change them to "x" and "y".
Solution by Addition or Subtraction Solution by Substitution
5a -2b = 3
2a - b = 0  

   5a -2b = 3
2(2a - b = 0)     multiply by 2

5a -2b = 3
4a -2b= 0     subtract

a = 3       answer for a

5a - 2b = 3   substitute to get answer for b
5(3) - 2b = 3
15 - 2b = 3
-2b = -12
b = 6

 

check:

 5a -2b = 3
2a - b = 0  

b = 2a   solve second equation for "b="

5a - 2(2a) = 3   substitute into the first 

5a - 4a = 3
a = 3   answer for a

5a - 2b = 3  substitute to get answer for b
5(3) - 2b = 3
15 - 2b = 3
-2b = -12
b = 6

 

check:
5a -2b = 3
5(3) -2(6) = 3
15 - 12 = 3
3 = 3 check!		 2a - b = 0  
2(3) - 6 = 0
6 - 6 = 0
0 = 0 check!  		 5a -2b = 3
5(3) -2(6) = 3
15 - 12 = 3
3 = 3 check!		 2a - b = 0  
2(3) - 6 = 0
6 - 6 = 0
0 = 0 check!  

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