find the value of X and Y..if 2X+3Y=[ 2 3 , 4 0 ] (2x2 matrix) and 3X+2Y=[ 2 -2 , -1 5 ] (2x2 matrix).

et 2x+3y=[ 2 3 , 4 0 ]-------(1)

3x+2y=[ 2 -1 , -1 5 ]------(2)

multiply the the equation (1) with 3.we get;

6x+9y=[ 6 9 , 12 0].-----(3)

then,multiply the equation (2) with 2.we get

6x+4y=[ 4 -4 , -2 10 ].----(4)

now subtract the equation (3) and (4)

(3)-(4).the we will get the answer as 5y=2 13 , 14 -10 ]

y=[ 2/5 13/5 , 14/5 -2 ]

now substitute the value of y in equation (1)

we get,2x+3[ 2/5 13/5 , 14/5 -2 ]=[ 2 3 , 4 0 ]

2x+[ 6/5 39/5 , 42/5 -6 ]=[ 2 3 , 4 0 ]

2x=[ 2 3 , 4 0 ]-[ 6/5 39/5 , 42/5 -6 ]

then 2x=[ 4/5 -24/5 , -22/5 6]

then x=[ 4/5 -24/5 , -22/5 6 ]/2

there fore x=[ 2/5 -12/5 , -11/5 3]

so x= 2/5 -12/5 , -11/5 3 ] and y=[ 2/5 13/5 , 14/5 -2 ]