Three roads join the junctions P, Q and R in a triangle…

Step 1. The matrix equation. $

=

$.

Step 2. The determinant. $1(1 - 0) - 1(0 - 1) + 0 = 2$, which is not $0$.

Step 3. The inverse. $A^{-1} = \dfrac{1}{2}

$.

Step 4. Multiply. $x = \tfrac{1}{2}(800 - 700 + 900) = 500$. $y = \tfrac{1}{2}(800 + 700 - 900) = 300$. $z = \tfrac{1}{2}(-800 + 700 + 900) = 400$.