Question 17310: {9x-y-2z=18
{5x-2y+z=10
{4x+y-3z=8 please help me with this
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! 9x-y-2z=18...........(1)
5x-2y+z=10...........(2)
4x+y-3z=8 ...........(3) ....we find that eqn(2)+eqn(3)gives us 9x-y-2z=18 which is same as (1)..so they are not independent equations .they are dependent equations and consistent in the sense that there are no contradictions.hence we get infinite solution for such a set of equations.we can give any value we like for one variable and solve the rest with that..say let us take x=0...so we get
-y-2z=18..........from (1)
y-3z=8.............from(3)
adding the above -5z=26..or...z=-26/5..substituting...
-y-2*(-26/5)=18
-y=18-52/5=(90-52)/5 = 38/5..or y=-38/5....so one solution set is
x=0;y=-38/5;and z=-26/5
like this we can get any number of solution sets by giving different vaslues to one variable and solving for the rest
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