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Solving Systems Using Matrices

OK, so to solve our equation, we had

AX = B

X = A^( -1 ) times B

 

So, let's findA^( -1 ) times B:

[ row 1: 8 row 2: -6 ] times [ row 1: ( 4 / 23 ) , ( 5 / 23 ) row 2: -( 3 / 23 ) , ( 2 / 23 ) ] = [ row 1: ( 2 / 23 ) row 2: -( 36 / 23 ) ] ... This is X

 

Remember what X is?

X = [ row 1: x row 2: y ] = [ row 1: ( 2 / 23 ) , -( 36 / 23 ) ]

So,x = ( 2 / 23 )andy = -( 36 / 23 )

 

The answer to our system is( 2 / 23 , -36 / 23 ).