Question

What is the solution of the system of equations?
-3x-4y-3z=-7
2x-6y+2z=3
5x-2y+5z=9

Answer 1

-3x-4y-3z=-7
2x-6y+2z=3
5x-2y+5z=9

multiply the first eq by -1
3x+4y+3z=7
2x-6y+2z=3
5x-2y+5z=9

multiply the first with 2 and the second with 3
6x+8y+6z=14
6x-18y+6z=9
5x-2y+ 5z = 9

subtract second eq from the first
6x+8y+6z=14
26y=5 => y = 5/26
5x-2y+ 5z = 9

substitute y in eq 1 and 3
3x+20/26+3z=14
y = 5/26
5x- 10/26+ 5z = 9

multiply the first by 5 and the third eq by 3
15x+100/26+15z=70
y = 5/26
15x- 30/26+ 15z = 27

substract the third eq from the first
130/26 = 43 which is false
so the system has no solution