Answer
$x=\frac{b+c}{2}$, $y=\frac{a+c}{2}$ and $z=\frac{a+b}{2}$
Work Step by Step
Step 1. Use elimination method: add up the first and second equations to get $2z=a+b$ thus $z=\frac{a+b}{2}$
Step 2. Add up the second and third equations to get $2x=b+c$ thus $x=\frac{b+c}{2}$
Step 3. Add up the first and third equations to get $2y=a+c$ thus $y=\frac{a+c}{2}$
Step 4. Conclusion: $x=\frac{b+c}{2}$, $y=\frac{a+c}{2}$ and $z=\frac{a+b}{2}$
