1. G RAPHING S YSTEMS OF E QUATIONS Lesson 6-1

2. _____________ equations together are called a _________ of ___________. If a system of equations has graphs that _______________ or __________________, then the system is said to be ____________________. If the graphs are ___________________ (which means they do_______ intersect), then the system of equation is said to be ___________________. If a system has exactly ______ solution, it is ___________________. (This is when the lines _____________________.) If the system has an _______________ number of solutions (as is the case with ________________ lines), then the system is ____________________. 2 or more system equations intersect crossconsistent parallel not inconsistent 1independent intersect infinite identical/same dependent

3. Use each graph to determine whether the system has no solution, one solution, or infinitely many solutions. A.y = –x + 4 y = –1 +1 Since the graphs are _________ there are ________ solutions. parallel no B.3x – 3y = 9 y = –x + 1 Since the graphs are ______________ lines, there is ______ solution (_________) intersecting 1 (2, -1)

5. Practice: 52y + 3x = 6 y = x – 1 6.y = x + 4 y = x – 1 7 2y + 3x = 6

6. Solve a System of Equations To solve a system of equations using graphing, Graph each equation in the system o If the lines intersect, there is one solution. The ______________ is the solution. o If the lines do not intersect, there is ____ solution. (____________ system.) o If the lines are the same, there are ____________ many solutions. intersection nodependent infinitely C.2x – y = –3 8x – 4y = –12 The graphs of the equations _______________. There are ______________________ solutions. are the same/identical. infinitely many

7. Graph each line (I used the slope and the y-intercept.) Find the intersection of the two lines. (This is the point that will satisfy both equations.) It is also your solution. The solution is (0, 3) y = 2x + 3 has a y-intercept at (0,3) Since the slope is 2, move up 2 and right 1 to get a second point, then draw a line through them.

8. Solve each equation for y and then graph it using the y-intercept and the slope or make a table to find points. x + 3y = 4 x – x + 3y = 4 – x 3y = 4 – x The two lines are parallel, so there is no solution.

9. F. Tyler and Pearl went on a 20 km bike ride that lasted 3 hours. Because there were many steep hills on the bike ride, they had to walk for most of the trip. Their walking speed was 4 km/hr. Their riding speed was 12 km/hr. How much time did they spend walking? x = time walking y = time riding x + y = 3 4x + 12y = 20 x + y = 3 x – x + y = 3 – x y = – x + 3 4x + 12y = 20 4x – 4x + 12y = 20 – 4x 12y = 20 – 4x The solution is (2, 1) which means they walked for 2 hours and rode bikes 1 hour.