x 3y 4z 17 4x y z 0 3x 4y 3z 15Solutionx 3y 4z 17 4x

x + 3y 4z = 17

4x y + z = 0

3x + 4y 3z = 15

Solution

x + 3y 4z = 17

4x y + z = 0

3x + 4y 3z = 15

Solve by gaussian elimination:

Multiply first equation by 4 and add the result to the second equation.

x + 3y 4z = 17

-13y + 17z =-68

3x + 4y 3z = 15

Multiply first equation by 3 and add the result to the third equation.

x + 3y 4z = 17

-13y + 17z =-68

-5y + 9z = -36

Multiply second equation by 5/13 and add the result to the third equation,

x + 3y 4z = 17

-13y + 17z =-68

32z/13 = -128/13

z= -4

solve for y: y=0

solve for x : x = 17 +4z = 17 + (-4*4) = 1

x= 1 ; y =0; z=-4