*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 can plot such functions using a planar graph; if a third dimension is added, we can still use aspect drawings to create the illusion of a three-dimensional graph.

Additional dimensions, however, become extremely difficult to visualize (spatially, our experience of the world is in three dimensions only).

First we started with Graphing Systems of Equations.

Then we moved onto solving systems using the Substitution Method.

In lesson 4, we solved some problems that involved two functions by equating the expressions.

Let's briefly look at an example again, but let's write it using our = 3 Solving the system of equations expressed in this manner is essentially the same, but we give it a slight twist.

Leave cells empty for variables, which do not participate in your equations.

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Level 1: Linear equations of the form ax = b Level 2: Linear equations of the form ax b = c Level 3: Linear equations with multiple variables and constant terms Level 4: Linear equations with variable expressions in the denominator of fractions An equation shows a relationship between two quantities that are of the same value. An equation consists of a left hand side (LHS) and a right hand side (RHS). In order to preserve the equality of the equation, whatever operations performed to the LHS must also be performed to the RHS. One method to solve an equation would be to separate the unknown from known values.

We move or keep the unknown on the left-hand side (LHS) of the equation and the known values on the right-hand side (RHS) of the equation like this: To do so, we need to perform some operations on both sides of the equation.

## Comments Systems Of Linear Equations And Problem Solving

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