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Solving Systems of Linear Equations using Substitution

Solving Systems of Linear Equations using Substitution 1.7 - Solution

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a

Let be the amount of blue paint he uses in the mix and be the amount of yellow paint. Since he needs to make a total of gallons of green paint, we can write the first equation as follows. We also know that he must use times more blue paint than yellow paint in the mix. We can write this as If we combine the equations, we have the following system of equations.

b
To find how much blue and how much yellow paint he uses in the mix, we have to solve the system for and Since is already isolated in Equation (II), we will substitute for in Equation (I) and solve the resulting equation for
Thus, Marcel must use gallons of yellow paint in the mix. Now, let's substitute for in Equation (II) to find
Thus, we have found that Marcel must use gallons of blue paint in addition to the gallons of yellow paint to make gallons of green paint.