The Mushrooms and 3-Bean Salad

30)  If 3 cans of mushrooms and 5 cans of 3-bean salad cost $5.90, and 2 cans
of mushrooms and 4 cans of 3-bean salad cost $4.52, then how much is each
can of mushrooms, and each can of 3-bean salad?

        x = can of mushrooms
        y = can of 3-bean salad


        3x + 5y = 5.90
        2x + 4y = 4.52

        Eliminate one of the variables by multiplying by a negative
        number.  We will multiply the bottom equation by -1.5:

        3x + 5y =  5.90
       -3x  -6y = -6.78
       ----------------
            -1y = -0.88

              y = 0.88 (a negative divided by a negative equals a positive)

       Plug the value of y into the equation to solve for x:

       (3x + 5y   = 5.90)

       3x + 4.40 = 5.90

       3x = 1.50

       x = 0.50

       Each can of mushrooms is 50 cents, and the 3-bean salad is 88 cents
       for each can.