a cash register contains $10 bills and $20 bills with the total value of $340. if there are 23 bills total then how many of each does the register contain

Say x is the amount of $10 bills and y is the amount of $20 bills

10x+20y=340

x+y=23

you would have to cancel out an x or y so let's cancel out the x

10x+20y=340

-10 (x+y=23)

which becomes

10x+20y=340

-10x-10y=230

which equals

0x+10y=110 or y=11

so there are 11 $20 bills ...

x+11=23

-11 - 11

x=12

which means there are 12 $10 bills

The answer is 11 $20 bills and 12 $10 bills