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#