Graphing Systems of Equations 6-1 Notes for Algebra 1 Graphing Systems of Equations

6-1 pg. 338 10-15, 19-23o, 27-41o, 54-75(x3)

System of Equations A system that contains 2 or more equations, the ordered pair that is its solution, is the solution to all equations in the system. A system can have 1 solution, many solutions, or no solutions.

Consistent/Inconsistent A system that has at least one solution./ the system has no solutions

Independent/dependent A consistent system has exactly one solution/ or infinite number of solutions.

Example 1 pg. 336 Number or solutions Use the graph to determine whether each system is consistent or inconsistent and if it is independent or dependent. 1.) 𝑦=−𝑥+1 𝑦=−𝑥+4 2.) 𝑦=𝑥−3 𝑦=−𝑥+1 6 5 4 3 2 1 -3 -2 -1 𝑦=−𝑥+4 𝑦=−𝑥+1 𝑦=𝑥−3

Example 1 pg. 336 Number or solutions Use the graph to determine whether each system is consistent or inconsistent and if it is independent or dependent. 1.) 𝑦=−𝑥+1 𝑦=−𝑥+4 Inconsistent 2.) 𝑦=𝑥−3 𝑦=−𝑥+1 Consistent and independent 6 5 4 3 2 1 -3 -2 -1 𝑦=−𝑥+4 𝑦=−𝑥+1 𝑦=𝑥−3

Example 2 pg. 336 Solve by graphing Graph each system and determine the number of solutions that it has. If it has one solution, name it. 1.) 𝑦=2𝑥+3 8𝑥−4𝑦=−12 2.) 𝑥−2𝑦=4 𝑥−2𝑦=−2

Example 2 pg. 336 Solve by graphing Graph each system and determine the number of solutions that it has. If it has one solution, name it. 1.) 𝑦=2𝑥+3 8𝑥−4𝑦=−12 Infinitely many solutions

Example 2 pg. 336 Solve by graphing Graph each system and determine the number of solutions that it has. If it has one solution, name it. 2.) 𝑥−2𝑦=4 𝑥−2𝑦=−2 No solutions 5 4 3 2 1 -4 -3 -2 -1

Example 3 pg. 337 Write and solve a system of equations Naresh rode 20 miles last week and plans to ride 35 miles per week. Diego rode 50 miles last week and plans to ride 25 miles per week. Predict the week in which Naresh and Diego will have ridden the same number of miles.

Example 3 pg. 337 Write and solve a system of equations 160 150 140 130 120 110 100 90 80 70 60 50 40 30 20 10 1 2 3 4 𝑦=25𝑥+50 Naresh rode 20 miles last week and plans to ride 35 miles per week. Diego rode 50 miles last week and plans to ride 25 miles per week. Predict the week in which Naresh and Diego will have ridden the same number of miles. Week 3 𝑦=35𝑥+20