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Solving Systems of Linear Equations using Substitution

a

In order to solve the given problem, we will form two equations and combine them into a system. We know that in the game there are point earning trees. If we let be the number of giant sequoias and be the number of baobab trees, we can write an equation to represent the situation. To finish the system we need another equation. Note, that if we add the number of giant sequoias multiplied by and the number of baobab trees multiplied by it will be equal to the number of points all trees are worth together. Using that the point earning trees in the game together are worth points we can write this equation. Combining the equations, we have the following system of equations.

b
To find how many giant sequoias and how many baobab trees there are in the game we will solve the system using the substitution method. As the first step we need to isolate one of the variables in one of the equations. Let's isolate in Equation (I). Next we will substitute for in Equation (II) and solve the resulting equation for
Now that we know that we can substitute this into either one of the equations in the given system. Let's use Equation (I).
The solution to the system of equations is and This means that there are giant sequoias and and baobab trees in the game.