So first, we gotta establish the 2 equations given to us which are:
[tex]2x+3y=175[/tex]
and
[tex]4x+y=125[/tex]
Assuming you'll need them solved, I gotchu.
So with the second equation I put down, subtract 4x on each side of the equation to get [tex]y=-4x+125[/tex] . Now with that equation, you are going to replace the y variable in the first equation and put in what y is equal to in the second equation.
And its gonna look like this [tex]2x+3(-4x+125)=175[/tex] .
Now foil 3(-4x+125), and it'll look like this [tex]2x-12x+375=175[/tex]
Combine like terms, and the equation should look like [tex]-10x+375=175[/tex] .
Subtract 375 on each side of the equation so that the equation is [tex]-10x=-200[/tex]
Divide -10 on each side, and you should get [tex]x=20[/tex] .
So now that we have gotten the price of the cassette, its much simpler to get the CD cost. Just replace the x variable with 20 in either equation.
[tex]4(20)+y=125[/tex]
[tex]80 + y = 125[/tex]
[tex]y = 45[/tex]
To sum up, cassettes are $20 and CDs are $45.
