Presentation on theme: "You will need: -Spiral/paper to take notes -A textbook (in this corner =>) -The Pre-AP agreement if you have it signed."— Presentation transcript:
1 You will need: -Spiral/paper to take notes -A textbook (in this corner =>) -The Pre-AP agreement if you have it signed
2 A point is a solution to a system of equation if the x- and y-values of the point satisfy both equations.Use substitution to determine if the given ordered pair is an element of the solution set for the system of equations.(1, 3);x – 3y = –83x + 2y = 9x – 3y = –8(1) –3(3)–83x + 2y = 93(1) +2(3)9Substitute 1 for x and 3for y in each equation.Because the point is a solution for both equations, it is a solution of the system.
3 Recall that you can use graphs or tables to find some of the solutions to a linear equation. You can do the same to find solutions to linear systems.
4 Example 2A: Solving Linear Systems by Using Graphs and Tables Use a graph and a table to solve the system. Check your answer.2x – 3y = 3y + 2 = xy= x – 2y= x – 1Solve each equation for y.
5 Example 2A ContinuedOn the graph, the lines appear to intersect at the ordered pair (3, 1)
6 The systems of equations in Example 2 have exactly one solution The systems of equations in Example 2 have exactly one solution. However, linear systems may also have infinitely many or no solutions.A consistent system is a set of equations or inequalities that has at least one solution, and an inconsistent system will have no solutions.
7 You can classify linear systems by comparing the slopes and y-intercepts of the equations. An independent system has equations with different slopes. A dependent system has equations with equal slopes and equal y-intercepts.
9 Example 3A: Classifying Linear System Classify the system and determine the number of solutions.x = 2y + 63x – 6y = 18y = x – 3The equations have the same slope andy-intercept and are graphed as the same line.Solve each equation for y.The system is consistent and dependent with infinitely many solutions.