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

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Answer 1 · 2014-10-20T14:12:41

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,

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

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

I hope that this was helpful.

How do I use Cramer's rule to solve the system of equations 3x-5y=-313x−5y=−313x-5y=-31 and 2x+y=12x+y=12x+y=1?