Question

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

Answer 1

`(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`