A particular color of paint requires a mix of five parts red, six parts yellow, and two parts black. Thomas does not have the pure colors available, but he finds three pre-mixed colors that he can use. The first is two parts red and four parts yellow; the second is one part red and two parts black; the third is three parts red, one part yellow, and one part black.
a. Write an equation that gives the correct portion of red by using the three available pre-mixed colors.
b. Write an equation that gives the correct portion of yellow and another equation that gives the correct portion of black.
c. Solve the systems of equations in 8a and b.