Pearson Algebra 2 Common Core, 2011
PA
Pearson Algebra 2 Common Core, 2011 View details
5. Systems With Three Variables
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Exercise 29 Page 172

When using the Substitution Method to solve a system of equations, it is necessary to isolate a variable.

Practice makes perfect
The given system consists of equations of planes. When using the Substitution Method to solve a system of equations, it is necessary to isolate a variable. In the second equation, it will be easiest to isolate
With a variable isolated in one of the equations, we can substitute its equivalent expression into the remaining equations. In the final step of the simplification of these substitutions, our goal is to have yet another variable isolated.

Simplify

Add and subtract terms

This time, the variable was isolated in the third equation. We can now substitute its equivalent expression into the first equation.
Solve by substitution
The value of is Substituting for into the third equation, we can find the value of
Now that we know the values of and we are able to find the value of
Simplify
The solution to the system is the point This is the singular point at which all three planes intersect. Let's check our solution by substituting the values into the system.

Substitute values

Multiply

Add and subtract terms

Since the substitution of our answers into the given equations resulted in three identities, we know that our solution is correct.