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If 2010a + 2014b = 2018 and 2012a + 2016b = 2020, what is the value of a - b?

 Jul 6, 2021
 #1
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By Cramer's rule, a = 1006 and b = -1003, so a - b = 2009.

 Jul 6, 2021
 #2
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2010a + 2014b = 2018         (1)

2012a + 2016b = 2020         (2)

 

Subtract:  (2) - (1)

2a + 2b = 2  or

a + b = 1                             (3)

 

so b = 1-a, put this into (1)

2010a +2014(1 - a) = 2018    Simplify:

-4a = 4

a = -1

put this back into (3) to find b, then find a - b.

 Jul 6, 2021

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