2. Chapter 2 Lesson 3 Systems of Linear Equations in Two Variables

3. Different methods of solving System of Equations in Two Variables  Graphically/Intersection  Substitution  Elimination

4. Solving a System of Equations Graphically  Get both equations into slope-intercept form  Y=mx+b  Graph both equations on your calculator  Y= menu  First equation in Y1  Second equation in Y2  Find their intersection  2 nd Trace  Option 5:intersection  Press ENTER 3 times  List X and Y values as an ordered pair

5. Examples

6. Solving System of Equations by Substitution  In one of the equations, solve for one of the variables  Doesn’t matter which one, pick whichever is easier  Substitute what that variable equals into the second equation for that variable  Has to be other equation, cannot use same equation  Solve for the remaining variable  Pick an equation to substitute the variable you solved for, solve for the other variable.  Doesn’t matter which equation, pick the easier one.

7. Examples

8. Solving a System of Equations by Elimination  Multiply one or both of the equations by a constant so that one of the variables has the same coefficient in both equations.  If the sign in front of the coefficient is the same in both equations, subtract one equation from the other.  If the sign in front of the coefficient is different in both equations, add the equations together.  Solve for the remaining variable.  In one of the equations, substitute the value in for the variable you solved for, then solve for the remaining variable.

9. Examples

10. Dependent and Inconsistent Systems  A system of equations has 3 possible outcomes.  1)The two equations will intersect at one point and have a unique solution.  2)The two equations will graph the same line resulting in an infinite number of solutions, this is called a dependent system.  3)The two equations are parallel and will never intersect, resulting in no solution, this is called an inconsistent system.

11. Examples

12. Homework  Page 137-141  1,3,6,9,11,13,15,17,19,21,23,26,31,33,37,38,41,43, 47,49,53,57,63,65