If a nurse has 20% alcohol solution and 70% alcohol solution, but needs 15 liters of a 40% alcohol solution, how do you think the nurse should proceed? Let’s use a system of linear equations and two different ways of solving this system of equations. First, we need to identify our variables, since we need to find out how much 20% alcohol solution (let’s call it Mixture A) and how much 70% alcohol solution (let’s call it Mixture B) we need.

Since our final mixture is a total of 15 liters, our first equation is A + B = 15.
Since our final mixture should have 40% alcohol solution, we need 6 liters of alcohol (.40*15) our second equation is 0.20A + 0.70B = 6.
Your job: Solve this system of equations for variables A and B by (1) graphing and by (2) either the substitution or substitution.