Answer:
1) Set up a system of equations. Assign each plant a variable. I used X for Daylillies and Y for Geraniums. In this case:
11x + 4y = 107
4x + 12y = 60
2) Get one variable by itsef. You can choose to either get the X or the Y by itself. For the sake of ease, I'll go with achieving X.
3) Using the equation 4x + 12y = 60, isolate the 4x.
4x = -12y + 60
4) Divide both sides by 4.
x = -3y + 15
5) X is isolated. Now plug in that isolated X into another remaining equation in order to isolate Y. Don't forget to combine like terms.
11(-3y + 15) + 4y = 107
-33y + 165 + 4y = 107
-29y + 165 = 107
-29y = -58
y = 2
6) You have your Y, which means that each Geranium costs $2 each. Now, you need to find X. Plug in Y into any of the first two equations that we started with.
4x + 12(2) = 60
4x + 24 = 60
4x = 36
x = 9
7) You now have both X and Y. Daylillies cost $9 each, and Geraniums cost $2 each.
8) You can double-check your answers by plugging in your final X and Y values into any of the first equations you wrote. If it comes out equal, it works.
