# Chapter 8 - Coordinate Geometry and Linear Systems - 8.6 - Elimination-by-Addition Method - Problem Set 8.6: 45

5 gallons of 10% and 15 gallons of 20%.

#### Work Step by Step

We call x the gallons of 10% solution and y the gallons of 20% solution. Thus, we obtain: $x + y = 20$ And $1.75 = (.1x + .2y )/2 \\ 3.5 = .1x + .2y$ 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 -10. Then, we add the two equations to obtain: $-15 = -y \\ y =15$ We plug in the given value into the top equation and solve for the other variable: $x +(15) = 20 \\ x =5$

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