Explanation:

The desired target expression is in three variables with unit coefficients of each. Instead of solving for three values individually by solving the three linear equations, we looked for creation of (x+y+z) by adding up the three equations. This is done in a few seconds by just adding up respective coefficients. Each of the three sets of coefficients summing up to the same value of 15, we can form the sum of the three equations as,
15(x+y+z)=45.
And so,
x+y+z−34=3−34=−31.
We call this process of collection of all similar terms as Principle of collection of friendly terms.