Question 1156489
<br>
There are three variables and only two equations.  Therefore we can't get a single solution; we can only get a family of solutions in terms of some parameter.<br>
The process is straightforward, although the calculations are generally a bit ugly.<br>
(1) Use elimination to reduce the system of 2 equations and 3 unknowns to a system of 1 equation with 2 unknowns.
(2) Solve that single equation for one variable in terms of the other.
(3) Substitute into either of the original equations to find an expression for the third variable.<br>
(1) I chose to eliminate x: multiply the first equation by 2 and the second equation by -3 and add:<br><pre>
  6x - 8y - 14z = -12
 -6x - 9y + 15z = -3
 ---------------------
     -17y +  z  = -15</pre>
Solve for z in terms of y:<pre>
             z = 17y - 15</pre>
(3) Substitute y for y and 17y-15 for z in one of the original equations to find x in terms of y:<br>
{{{2x+3y-5(17y-15) = 1}}}<br>
{{{2x+3y-85y+75 = 1}}}<br>
{{{2x = 82y-74}}}<br>
{{{x = 41y-37}}}<br>
ANSWER:
x = 41y-37; y = y; z = 17y - 15<br>
Choose any number for the "parameter" y and use it to find values for x and z.  Those values of x, y, and z will satisfy both of the given equations.<br>