8x - y +z = -9, 2x = 2y -3z = -22, x-3y 2z =15 solve for an ordered tripple

Question

8x - y + z = -9

2x + 2y - 3z = -22

x - 3y + 2z = 15

Answer 1

Label the equations A, B, C.

2A+B: 18x-z=-40. So x=(z-40)/18.

B-2C: 8y-7z=-52. So y=(7z-52)/8.

We have x and y in terms of z so we can substitute for x and y in any equation, so we choose A:

8(z-40)/18-(7z-52)/8+z=-9; (4z-160)/9-(7z-52)/8+z=-9;

Multiply through by 8*9=72:

8(4z-160)-9(7z-52)+72z=-648; 32z-1280-63z+468+72z=-648.

41z=164, so z=4. Therefore x=-36/18=-2 and y=-24/8=-3.

Check out solution in all original equations:

-16+3+4=-9; -4-6-12=-22; -2+9+8=15. Solution is (-2,-3,4).

More...