Question 1167063
so Im trying to brush up on my skills and have been presented with: 

x - y - z = 5
y - x - z = 1
z - y - x = -15
x * y - z = a 

so far all I can remember is to equal everything out to zero leaving: 

x - y - z - 5 = 0
y - x - z - 1 = 0
z - y - x + 15 = 0
x * y - z - a = 0
what kind of problem is this exactly and how do I solve he variables?
<pre>This is a system of equations in 3 VARIABLES. You need to find the value of each of the 3 variables....in this case, x, y, and z. Then determine the value of a, which is: x * y - z.
 
There're may ways that this system can be solved. The easiest, in my opinion, is the following:
x - y - z = 5 -------- eq (i)
y - x - z = 1 -------- eq (ii)
z - y - x = -15 ------ eq (iii)

Rearrange eqs (ii) & (iii) to get: {{{matrix(3,6, x - y - z, "=", 5, "-----", eq, "(i)", - x + y - z, "=", 1, "------", eq, "(ii)", - x - y + z, "=", - 15, "-----", eq, "(iii)")}}}
- 2z = 6 ----- Adding eqs (i) & (ii)
{{{highlight_green(matrix(1,5, z, "=", 6/(- 2), "=", - 3))}}}


- 2x = - 14 ----- Adding eqs (ii) & (iii)
{{{highlight_green(matrix(1,5, x, "=", (- 14)/(- 2), "=", 7))}}}


y - 7 - (- 3) = 1 ------ Substituting 7 of x, and - 3 for z in eq (ii)
y - 7 + 3 = 1
y - 4 = 1
{{{highlight_green(matrix(1,5, y, "=", 1 + 4, "=", 5))}}}

Shouldn't pose a problem now, to find "a."</pre>