Connecting a DVD player to a television set requires a cable with special connectors at both ends. You buy a six-foot cable for $15.50 and a three-foot cable for $10.25. Assuming that the cost of a cable is the sum of the cost of the two connectors and the cost of the cable itself, what is the cost of a four-foot cable?

So a 3 foot cable is10.25

a 6foot cable is 15.50

so

x=cost per foot

y=cost of special connectors

3x+y=10.25

6x+y=15.50

make first equation negative and add to the first

3x=5.25

divide both sides by 3

1.75=x

so it costs 1.75 for a foot of cable

subtitue into first equation

3 (1.75) + y=10.25

5.25+y=10.25

subtract 5.25 from both sides

y=5 dollars=cost of special so

4x+y=4 (1.75) + 5=7+5=$12

so the cost of a 4 foot cable is $12