To solve for x and y using the elimination method, we will multiply both sides of the matrix equation by the inverse of the coefficient matrix:
(1/2 -1/4) (x) = (2)
(2/5 1/6) (y) (6)
The inverse of the coefficient matrix is:
( 4/1 2/1 )
(-5/2 -5/1 )
Multiplying both sides of the equation by the inverse matrix, we get:
( 4/1 2/1 ) (1/2 -1/4) (x) = ( 4/1 2/1 ) (2)
(-5/2 -5/1 ) (2/5 1/6) (y) (-5/2 -5/1 ) (6)
Simplifying, we have:
( 1 0 ) (x) = ( 8 )
( 0 1 ) (y) ( -12 )
This gives us the following equations:
x = 8
y = -12
Therefore, the solution to the matrix equation is x = 8 and y = -12.
Solve for x and y in the following matrix equation using elimination method
(1/2 -1/4) (x) =(2)
(2/5 1/6).( y). 6
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