Please help me

Adding the last three equations, we get [(p + q + r) + (q + r)x + (p + r)y + (p + q)z = x + y + z.]Substituting p+q+r=−3, we get −3+(q+r)x+(p+r)y+(p+q)z=x+y+z.

Manipulating the first equation and substituting, we get \begin{align*} -3 + (-3 - p)x + (-3 - q)y + (-3 - r)z &= x + y + z \ \Rightarrow \quad -3 - px - qy - rz &= x + 3x + y + 3y + z + 3z \ \Rightarrow \quad -3 - (px + qy + rz) &= 4 (x + y + z) \ \Rightarrow \quad x + y + z &= \frac{-2}{4} = -\frac{1}{2}. \end{align*}

Therefore, x+y+z=−1/2.​​

Nice try, but that's not correct...

It's actually -1

Add the top four equations and you get

\(p(1+x+y+z)+q(1+x+y+z)+r(1+x+y+z)=1+x+y+z\)

so

\(p+q+r=1,\)

implying that the equations are inconsistent.