1. Section 3.1 Introduction to Systems of Equations  Any pair of Linear Equations can be a System  A Solution Point must make both equations true  When plotted on the same graph, the solution is the point where the lines cross (intersection)  Some systems do not have a solution 3.11

2. System of Two Equations Solution point (3,0) Please Note: I use A and B notation, different from the (1) (2) used in your text 3.12

3. Why Study Systems of Equations? We will first study systems of 2 equations in 2 unknowns (usually x and y) The methods we use to solve them will also be useful in higher degree systems that involve quadratic equations or systems of 3 equations in 3 unknowns 3.13

4. Find the Equations: Put Data into Tables or Formulas ____(p)ostcard stamps and ____ (f)irst-class stamps were bought Guessing … How about 100 first class stamps? Guessing … How about 70 first class stamps and 50 postcard stamps? 37(70)= 2590 23(50)= 1150 sum is 3740 ! Oops, we need a better way 37(100)=$37.00 Oops, way too much! 3.14

5. Find the Equations: Separate Data from Noise Americans bought ____ gal (w)ater and ____ gal of (s)oft drinks 3.15

6. Checking a Proposed Solution 3.16

7. Approximation … Solving Systems Graphically 3.17

8. Practice – Solving by Graphing Consistent: (1,2) Inconsistent: no solutions Consistent: infinite sol’s 3.18

9. Find the Intersection: Put Data into Tables or Formulas ____(p)ostcard stamps and ____ (f)irst-class stamps were bought 3.19

10. And furthermore …  Section 3.2 Solving by Substitution or Elimination Section 3.2 Solving by Substitution or Elimination 3.110