Okay so to represent juice we are going to use X, and to represent water we are going to use Y.
We also know that the first two starting equations are:
6x + y = 135
4x + 2y = 110
We can re-arrange the first equation so that it equals y (for now), so it is going to end up looking like this:
y = -6x +135
Now you can take that equation and plug into either one of the starting two equations. I chose the second equation. We just substitute what y equals in for y in the equation, so we have:
4x + 2(135 - 6x) = 110
Now solve
4x + 270 -12x = 110
-8x + 270 = 110
Subtract 270 from both sides
-8x = -160
Now divide by -8 on both sides
x = 20
We can now confirm that juice costs $20
Now lets plug that into the equation where we solved for y, to get the actual value of y.
y = 135 - 6(20)
y = 135 - 120
y = 15
The price of water costs $15
From this we can conclude that the cost of juice is $20 and the price of water is $15
