Pearson Algebra 2 Common Core, 2011
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Pearson Algebra 2 Common Core, 2011 View details
5. Systems With Three Variables
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Exercise 9 Page 171

The given system consists of equations of planes. Notice that the coefficients of in the first and the third equations are the additive inverse of the coefficient of in the second equation; they will add to be Let's use the Elimination Method to find a solution to this system.
We can start by adding the second equation to the first and the third equations to eliminate the

Add

Remove parentheses

Add and subtract terms

Next, we will use our two equations that are only in terms of and to solve for the value of one of the variables. We will once again apply the Elimination Method, but this time it will be similar to when using it in a system with only two variables.
Solve by elimination
Now that we know that we can substitute it into the first equation to find the value of
Solve for
The value of is Let's substitute both values into the second equation to find
Solve for
The solution to the system is This is the singular point at which all three planes intersect. Now we can 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.