If 2010a + 2014b = 2018 and 2012a + 2016b = 2020, what is the value of a - b?
By Cramer's rule, a = 1006 and b = -1003, so a - b = 2009.
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.
