## Elementary Algebra

We call x the Liters of 50% solution and y the Liters of 80% solution. Thus, we obtain: $x + y = 10.5$ And $.7 = (.5x + .8y )/10.5 \\ 7.35 = .5x + .8y$ In order to solve this problem, we multiply one or both of the equations by a value that will make one of the variables cancel. We multiply the top equation by 1, and we multiply the bottom equation by -2. Then, we add the two equations to obtain: $-4.2 = -.6y \\ y =7$ We plug in the given value into the top equation and solve for the other variable: $x +(7) = 10.5 \\ x =3.5$