find X AND Y, if 2x+3y=[2 3 ] 3X+2Y=[ 2 -2 ]

[ 40] and [ -15 ]

let 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 the value of x= 2/5 -12/5 , -11/5 3 ]..and the value of y=[ 2/5 13/5 , 14/5 -2 ].

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