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

1 answer

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.