Systems Of Linear Equations And Problem Solving

Systems Of Linear Equations And Problem Solving-29
The following videos will show four types of linear equations and how to solve each type.

The following videos will show four types of linear equations and how to solve each type.

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Although an additional variable (z) is added, the concepts and method of solution are all the same.

Each equation can be graphed using an aspect drawing as a plane.

4) notation of (4, 0, 0), (0, –4, 0), and (0, 0 ,4). To solve, we once again choose an equation, solve for a variable, then substitute to eliminate that variable from the resulting expression.

We must perform this process three times to reduce the system of equations to an equation in one variable.

You can use other methods to solve such problems, but (as mentioned previously) some of them would require an entire course to flesh out adequately.

Nevertheless, the substitution method is perhaps the most lucid method for learning how to solve these types of problems. From the lesson, recall that this expression corresponds to a plane, and we can plot it by finding the intercepts and then connecting them.

First we started with Graphing Systems of Equations.

Then we moved onto solving systems using the Substitution Method.

We can solve just one of the equations for one variable or the other (usually whichever is easiest) and then use substitution to eliminate one variable from the other equation. We can check this result by substituting these values back into the original equations.

This leaves an equation in one variable that can then be solved to find part of the solution. Let's now take a look at a system of equations in three variables.

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