Solve the system xyz0 x2y3z3 2x3y4z3Solutionxyz0 x2y3z3 2x3y

Solve the system

x+y-z=0

x+2y-3z=-3

2x+3y-4z=-3

Solution

x+y-z=0

x+2y-3z=-3

2x+3y-4z=-3

Multiply equation first by -3 and add it to second we get

-3x-3y+3z+x + 2y -3z=-3

-2x -y=-3   equation 4

Multiply first by -4 and add it to third, we get

-4x-4y+4z+2x+3y-4z=-3

-2x -y=-3 equation 5

So here we have same equations in both equation 4 and 5

So we have infinite solutions .