10 Points Linear Equation of Matrix?

4x + 3y + z = 1 ------(1)
3x - 2y - 3z = -2 -----(2)
5x + 4y + 2z = 3 ---(3)

Multiply equation (1) by 3
12x+9y+3z = 3
3x - 2y - 3z = -2 -----(2)

add:
15x+7y = 1 -----------(4)

Multiply equation (2) by 2 and equation (3) by 3
6x-4y-6z = -4
15x+12y+6z = 9

add:
21x+8y= 5 -----------(5)

solve (4) & (5)
15x+7y = 1 -----------(4)
21x+8y= 5 -----------(5)

Multiply equation (4) by -8 and equation (5) by 7
-120x-56y =-8
147x+56y =35

Add:
27x = 27
x = 1 ( x solved)
15x+7y = 1 ------(4)
15(1) + 7y = 1
7y = -14
y = -2 ( y solved)

4x + 3y + z = 1 ------(1)
4(1)+3(-2) + z = 1
4-6 + z = 1
-2+z = 1
z = 3 ( z solved)

x=1; y = -2; z=3

its equals to 0