1. 10-1 An Introduction to Systems A _______ is a set of sentences joined by the word ____ or by a ________________. Together these sentences describe a ______ ________. An Example 3x - 2y = 6 4x + 5y = 7 { What is the solution to a system? Since this system has 2 variables it is a _______________. On a graph, it’s the point of __________, an ___________.

2. 1. Verify that is the solution to the system 44 _ 3 23, ( ) 3x - 2y = 6 4x + 5y = 7 { See if the ordered pair works in each sentence. 3x - 2y = 6 3· - 2 = 6 44 23 · - 3 23 132 23 + 6 23 = 6 138 23 = 6 6 = 6 4x + 5y = 7 4· + 5· = 7 44 23 - 3 23 176 23 + - 15 23 = 7 161 23 = 7 7 = 7

3. 2. The sum of 2 #s is 14 and their product is 40. a. What system can be solved to find the #s ? b. Graph each equation. What are the numbers? 20 - 16 - 12 - 8 - 4 - 4 8 12 16 20 y x The solution to the system is

4. 3. Solve by graphing. Find all solutions to the system y = -3x + 1 -2x + 2y = -14 { 1 - - - 2 4 6 -2 - - -4 - - -6 - - The solution to this system is y x