Answer
$5$ new games were rented.
Work Step by Step
Step $1$
Write the system of equations.
Let x = number of old games, y = number of new games.
You rented 6 video games:$\quad x+y=6$
The cost was $ {{\$}} 22:\qquad 2x+4y=22$
Step $2$
Solve one of the equations for one of the variables.
$x+y=6\quad\Rightarrow\quad y=6-x$
Step $3$
Substitute $6-x$ for $y$ in the other equation and solve for $x$
$2x+4y=22$
$2x+4(6-x)=22\quad $... simplify
$ 2x+24-4x=22\quad$ ... subtract 24
$-2x=-2\quad $... divide with -2
$x=1$
Step $4$
Substitute $1$ for $x$ in$\quad x+y=6 \quad $and solve for $y$.
$y+1=6$
$y=5$
Reverting back to the meaning of x and y,
1 old game was rented, and $5$ new games were rented.
