How do I use Cramer's rule to solve the system of equations #3x-5y=-31# and #2x+y=1#?

1 Answer
Oct 20, 2014

Convert the system of linear equations

#{(3x-5y=-31),(2x+y=1):}#

into the matrix equation

#[(3" "-5),(2" "" "1)][(x),(y)]=[(-31),(1)]#.

Let u s now find the necessary determinants

The determinant of the coefficient matrix is

#|(3" "-5),(2" "" "1)|=3cdot1-(-5)cdot2=13#

By replacing the first column by the right-hand side,

#|(-31" "-5),(" "1" "" "1)|=(-31)cdot1-(-5)cdot1=-26#.

By replacing the second column by the right-hand side,

#|(3" "-31),(2" "" "1)|=3cdot1-(-31)cdot2=65#

By Cramer's Rule,

#{(x={-26}/{13}=-2), (y={65}/{13}=5):}#


I hope that this was helpful.