1) Let's set the system of linear equations:
x +2y -3z = a
-x -y +z = b
2x +3y -2z =c
2) Since the solution has already been given ( -1,2,-3) all that's left to do, is to plug it into each equation so that we can find a, b and c. Just like this:
x +2y - 3z = a ⇒ (-1) +2(2) -3(-3) = a ∴ a = 4
-x -y +z = b ⇒ -(-1) -(2) +(-3) = b ∴ b = 0
2x +3y -2z =c ⇒ 2(-1) +3(2) -2 (-3)=c ∴ c = -2
3) Hence, a = 4 b = 0 and c = -2
