Problem 14
we have
-5x+3y+6z=4 -------> equation 1
-3x+y+5z=-5 -------> equation 2
-4x+2y+z=13 ------> equation 3
step 1
In the equation 3 isolate the variable z
-4x+2y+z=13
z=-4x-2y+13 --------> equation 4
step 2
Substitute equation 4 in equation 1
-5x+3y+6(-4x-2y+13)=4
-5x+3y-24x-12y+78=4
-29x-9y=-74 ----------> equation 5
step 3
substitute equation 4 in equation 2
-3x+y+5(-4x-2y+13)=-5
-3x+y-20x-10y+65=-5
-23x-9y=-70 -------> equation 6
step 4
Solve the system of equations 5 and 6
-29x-9y=-74 ----------> equation 5
-23x-9y=-70 -------> equation 6
Multiply equation 6 by -1
-1*{-23x-9y=-70} -------> 23x+9y=70 -------> equation 7
step 5
Adds equation 5 and equation 7
-29x-9y=-74
23x+9y=70
--------------------
-6x=-4
x=4/6
x=2/3
step 6
Find the value of y
substitute the value of x in equation 5 or equation 7