1. 3-2 Solving Systems Algebraically

2. In addition to graphing, which we looked at earlier, we will explore two other methods of solving systems of equations. SUBSTITUTION METHOD ELIMINATION METHOD These are processes for solving both equations at the same time. Graphs can be helpful, but are not required to find a solution. You will be responsible for solving systems using all methods.

3. Solve one of the equations for either x or y (you pick) SUBSTITUTE the expression you get into the other equation Solve that equation for the remaining variable Substitute the value you just obtained back into either of the original equations The Solution to the system is (6,-7) The system is consistent and independent

4. Solve one of the equations for either x or y (you pick) SUBSTITUTE the expression you get into the other equation Solve that equation for the remaining variable Substitute the value you just obtained back into either of the original equations

5. The solution to the system is (7,0) The system is consistent and independent

6. Put both equations in standard form Get one of the variables to have the same coefficient in both equations Add (or subtract) the equations to ELIMINATE that variable. Solve the new equation for the remaining variable. Substitute the value you just obtained back into either of the original equations **Get the coefficients of y the same** The solution is (6,-7) The system is consistent and independent

7. Put both equations in standard form Get one of the variables to have the same coefficient in both equations Add (or subtract) the equations to ELIMINATE that variable. Solve the new equation for the remaining variable. Substitute the value you just obtained back into either of the original equations *Eliminate x

8. The solution is (-1,-1) The system is consistent and independent

9. All variables are eliminated End result is an equation that is NOT TRUE “No Solution” The equations represent parallel lines The system is INCONSISTENT All variables are eliminated End result is an equation that IS TRUE Infinite solutions (write your answer as the equation of a line) The equations represent overlapping lines The system is consistent and DEPENDENT

10. How will you decide which to use? When is substitution easier? When is elimination easier? When is graphing (or using a table) easier?