3.2+SOLVE+LINEAR+SYSTEMS+ALGEBRAICALLY

3.2 Solving Linear Systems Algebraically

THE BIG IDEAS FOR THIS CHAPTER:

 * == Solving systems of equations using a variety of methods. ==
 * Graphing systems of equations and equalities.
 * Using matrices.

- in the real world, you can use linear equations to solve real-world problems.
-Like showing the guy you work for your skills and make a graph for the stats.

KEY VOCABULARY:

 * ** SUBSTITUTION METHOD: a method of solving a system of equations by solving one of the equations for one of the variables and then substituting the resulting expression in the other equations. **
 * ** ELIMINATION METHOD: a method of solving a system of equations by constants, then adding the revised equations to eliminate a variable. **

Step 1 ** : ** Solve one of the equations for one of its variables. Step 2 ** : ** Substitute the expression from Step 1 into the other equation and solve for the other variable. Step 3 ** : ** Substitute the value from Step 2 into the revised equation from Step 1 and solve.
 * EXAMPLE #1: **
 * 1: Substitution method: **


 * Applying the steps: **
 * EQUATION 1: 2X+5Y=-5 **
 * EQUATION 2: X+3Y=3 **

Step 1 :** Solve equation 2 for X. **
 * X=-3y+3 **

Step 2 : ** Substitute the expression for X into equation 1 and solve for Y. **
 * 2x+5y=-5 WRITE EQUATION 1 **
 * 2(-3y+3)+5y=-5 SUBSTITUTE -3y+3 for X. **
 * y=11 SOLVE FOR Y. **

Step 3 :** Substitute the value Y into revised equation and solve for X. **
 * X=-3y+3 WRITE REVISED EQUATION 2. **
 * X=-3(11)+3 SUBSTITUTE FOR Y. **
 * X=-30 SIMPLIFY. **


 * The Solution for the system is (-30, 11) **

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