Question

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

Answer 1

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):}#

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I hope that this was helpful.