blank notes solving systems of equations by graphing

1. SOLVE SYSTEMS OF
EQUATIONS BY
GRAPHING
SECTION 6.1 PAGES 335-343

2. SYSTEM OF EQUATIONS
• A group of two or more equations
• The solution to the system of equations is the overlap (where the lines cross)
• The solution to the system of equations is the point the equations have in
common.
• Three possible cases for the solution
• Exactly One Soltuion
• Infinite Solutions
• No Solution

3. EXACTLY ONE SOLUTION
• Cross at one point
• That point is the solution
• Consistent
• Independent

4. INFINITE SOLUTIONS
• Same line – Lines on top of each other
• Infinite solutions NOT All Real Numbers
• Solutions must come as ordered pairs
• Consistent
• Dependent

5. NO SOLUTION
• Parallel Lines
• Lines will never cross
• No Solution can exist
• Inconsistent

6. GRAPHING AS A WAY TO SOLVE
• Easy to set up
• Simplest to find the solution
• Must be accurate
• Does not usually work out nice

7. Solve the system
𝑦 = −3𝑥 + 10
𝑦 = 𝑥 − 2

8. Solve the System
2𝑥 − 𝑦 = −1
4𝑥 − 2𝑦 = 6

9. 𝑆𝑜𝑙𝑣𝑒 𝑡ℎ𝑒 𝑆𝑦𝑠𝑡𝑒𝑚
𝑦 = −2𝑥 − 3
6𝑥 + 3𝑦 = −9

10. Homework
Page 339 #27-38