How do you solve #2x+4y=10, 6x+2y=10# using Cramer's rule?

1 Answer
Alan P.
Mar 2, 2017

#(x,y)=(1,2)#
#color(white)("XXX")#see below for determination using Cramer's Rule.

Explanation:

Re-writing the given equations as an augmented matrix:
#color(white)("XXX")( (2,4,"|",10),(6,2,"|",10))#

and using the standard derived square matrices:
#M=((2,4),(6,2)),M_x=((10,4),(10,2)),M_y=((2,10),(6,10))#

We can calculate the Determinants:
#color(white)("XXX")D_(M)=2xx2-6xx4=-20#
#color(white)("XXX")D_(M_x)=10xx2-10xx4=-20#
#color(white)("XXX")D_(M_y)=2xx10-6xx10=-40#

Cramer's Rule Tells us:
#color(white)("XXX")x=(D_(M_x))/(D_M)=(-20)/(-20)=1#
and
#color(white)("XXX")y=(D_(M_y))/(D_M)=(-40)/(-20)=2#

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