How do you solve $3x + 4y = 24$ and $6x - 1y = 21$ using matrices?

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Answer 1 · 2016-08-30T06:42:38

$x=4, y=3$

First let's build the matrix by filling its rows by the coefficients of the system in its standard form:

$D=((3,4),(6,-1))=3(-1)-4(6)=-3-24=-27$

Then you build the matrices $D_x$ and $D_y$ by substituting the known terms in the first and the second column, respectively:

$D_x=((24,4),(21,-1))=24(-1)-4(21)=-24-84=-108$

$D_y=((3,6),(24,21))=3(21)-6(24)=63-144=-81$

Then you can solve by calculating:

$x=(D_x)/D=(-108)/(-27)=4$

$y=(D_y)/D=(-81)/(-27)=3$

How do you solve 3x + 4y = 24 3x + 4y = 24 and 6x - 1y = 216x - 1y = 21 using matrices?