Isolate First

Sometimes neither equation has a variable alone on one side. Then you isolate a variable first, and substitute after that. In the system $x-y = 1;\quad 2x+y = 8$, add $y$ to both sides of the first equation to get $x = y+1$. Replace $x$ in the second equation with $y+1$: $2\left(y+1\right)+y = 8$. Expand and collect the terms to get $3y = 6$, so $y = 2$. Then $x = 2+1$, so $x = 3$.

When possible, isolate a variable with coefficient 1 or -1. This avoids introducing fractions during that step. Isolating the variable in $2x$ also works, but requires dividing the other terms by 2.