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Solving Systems of Linear Equations using Substitution

Solving Systems of Linear Equations using Substitution 1.8 - Solution

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a

Let be the number of backpacks with tent and be the number of warm hiking clothes they rent. Since they in total rent items, we can write the first equation as: We also know that the hikers spend to rent equipment from Norgay High Altitute Hiking. Additionally, a backpack+tent, costs and a set of warm hiking clothes, costs We can write this as the equation: Combining the equations, we have the following system of equations:

b
To find how many backpack+tents and how many sets of warm hiking clothes the group of hikers rent, we have to solve the system for and We will use the substitution method. In order to use it, we need one of the variables isolated. Let's isolate in Equation (I). Now we can substitute for in Equation (II) and solve the resulting equation for
Now we can find by substituting for in Equation (I) and solve the resulting equation for
Thus, the hikers rents backpacks+tents and sets of warm hiking clothes.