Question

X+Y-Z=19 2X-3Y+Z=13 3X-5Y-6Z=-15

Answer 1

A suitable graphing caculator gives the result

X = 15 25/39

Y = 7 6/13

Z = 4 4/39

_____

If you want to solve this by hand, you can add 3 times the first equation to the second to get

... 5X -2Z = 70

and 5 times the first equation to the third to get

... 8X -11Z = 80

Then Cramer's Rule tells you the solutions for X and Z are

... X = (-160+770)/(-16+55) = 610/39

... Z = (560 -400)/39 = 160/39

From there, you can substitute into any of the equations to find Y. The first one might be most convenient.

... Y = 19 -X +Z = 19 -(15 25/39) +(4 4/39) = 8 -21/39 = 7 6/13