Substitution

Substitution is a way to solve a system when one equation already tells you what a variable equals. You replace that variable in the other equation with the expression it equals. In the system $y = 2x-1;\quad x+y = 5$, the first equation says that $y$ equals $2x-1$. Replace $y$ in the second equation with $2x-1$. The result is one equation with one variable:

$$x+2x-1 = 5$$

$$3x-1 = 5$$

$$x = 2$$

Now put $x = 2$ into the first equation to find $y$: $y = 2\cdot 2-1$, so $y = 3$. The solution is the pair $x = 2$, $y = 3$. Substitution gives the exact point where the two lines cross, without drawing them.

Substitution is convenient when one equation already has a variable isolated. Replace that variable in the other equation with the expression it equals.