How do you solve the following system?: #-x -2y =-1, 6x -y = -4#

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Answer 1 · 2016-01-18T11:40:19

#x = 7/13# and #y = 10/13#

By Cramer's rule:

Make a matrix with the coefficient of each columns, in this case

#[(-1,-2),(6,-1)]#

Take the determinant of this

#|(-1,-2),(6,-1)| = 13#

Now replace the first row with the results row

#[(-1,-2),(-4,-1)]#

Now take this determinant

#|(-1,-2),(-4,-1)| = 7#

The ratio of these determinants is the solution for #x#, so

#x = 7/13#

Replace the #y# row by the results row

#[(-1,-1),(6,-4)]#

Take this determinant

#|(-1,-1),(6,-4)| = 10#

Like before the ratio is the answer for #y#

#y = 10/13#