How do you solve 2x+4y=10, 6x+2y=102x+4y=10,6x+2y=10 using Cramer's rule?

1 Answer
Mar 2, 2017

(x,y)=(1,2)(x,y)=(1,2)
color(white)("XXX")XXXsee 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