1. Linear Systems

2. Chapter Learning Objectives
Students will:
-Solve linear systems consisting of two simultaneous equations in two variables using algebraic elimination
-Graph linear equalities in two variables
-Graph linear systems consisting of two linear relations in two variables
-Solve problems by setting up systems of linear equations in two variables.

3. Terminology Review
Variable: unknown quantity (it can vary/change) represented by an alphabetical letter. E.g. “x” or “y” are commonly used.
Coefficient: Number which precedes a variable. E.g. in the expression “4x”, 4 is the coefficient.
Equation: a mathematical statement that contains an equals sign. E.g. “x+2=4” is an equation, “x+2” is an expression.
Systems of Equations:
a collection of two or more equations with a same set of unknowns. In solving a system of equations, we try to find values for each of the unknowns that will satisfy every equation in the system.

4. In order to solve systems if equations, the easiest way to do so is to Eliminate a variable OR manipulate one of the equations so that one variable is written in terms of the other- WHAT?
To eliminate a variable: means to take away a variable from the system
To manipulate: to move the terms in an equation so that you end up with an equation which reads, “x= “ or “y= “
When presented with a system of equations:
Step 1: Ask yourself- Can I eliminate a variable, or do I have to manipulate an equation?

5. So, to eliminate, or manipulate: That is the question!
Step 1: Check to see if a variable can be eliminated by adding equations together: x + y= 1 x – y= 7 2x = 8 Add equations together and solve for unknown: Step 2: Plug in the known value for the variable to solve for the unknown:

6. If a variable cannot be eliminated by adding equations.
E.g.
x - 3y = -12
3x + y = 6
*Adding these equations together will not eliminate a variable- we must manipulate!

7. Step 1: Manipulate one of the equations so that you end up with an x or y statement.
Step 2: substitute/plug in this value in for “x” in the second equation.
Step 3: Plug in/ substitute known value to one of the equations