2.  Systems of equations- two equations together  A solution of a system of equations is an ordered pair that satisfies both equations  Consistent- the graphs of the equations intersect  If consistent with exactly 1 solution = independent  If consistent with infinite solutions = dependent  Inconsistent- the graphs of the equations are parallel  No ordered pair solutions Exactly one solution Infinite solutions No solutions Consistent and Independent Consistent and Dependent Inconsistent 3.1

3. Ex: Solve by graphing y = -x + 8 y = 4x - 7 *See teacher or other student class for work on these examples

4. Ex #2. Solve by graphing x + 2y = 5 2x + 4y = 2 *See teacher or other student class for work on these examples

5.  Substitution Method: used when one equation can be solved for a variable.  When one variable has a coefficient of 1 or -1  Elimination Method: used when the two equations have the same coefficient for one of the variables (you can add or subtract right away to cancel one variable)  Elimination with Multiplication Method: used when substitution and elimination don’t work 3.2

6.  Substitution x + 5y = -3 3x – 2y = 8

7.  Infinite or No solutions 6x – 2y = -4 y = 3x + 2  Write and solve a System of Equations The New York Yankees and Cincinnati Reds together have won a total 31 World Series. The Yankees have won 5.2 times as many as the Reds. How many have each team won? 6x – 2(3x +2) = -4 6x – 6x - 4 = -4 -4 = -4 When all variables cancel, if: the statement is true = infinite solutions the statement is false = no solutions Infinite solutions

8.  Elimination 5s + 2t = 6 9s + 2t = 22

9.  Write and solve a system of equations Twice one number added to another number is 18. Four times the first number minus the other number is 12. Find the numbers.

10.  Multiply One Equation 3x + 4y = 6 5x + 2y = -4  Multiply Two Equations 3x + 4y = -25 2x – 3y = 6 Multiply one equation to make a variable have the same number and opposite sign Multiply both equations to make a variable have the same number and opposite sign

11. 1. get the inequality in slope-intercept from 2. Graph the intercept and use slope to find the next points 3. Draw the line: = dotted, or = solid 4. If needed: Test an ordered pair not on the line -if true, shade that side of the line -if false, shade the other side of the line 5. Repeat steps 1-4 for the second inequality. 3.3