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Published byDulcie Booker Modified over 6 years ago

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You will need: -Spiral/paper to take notes -A textbook (in this corner =>) -The Pre-AP agreement if you have it signed

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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 = –8 3x + 2y = 9 x – 3y = –8 (1) –3(3) –8 3x + 2y = 9 3(1) +2(3) 9 Substitute 1 for x and 3 for y in each equation. Because the point is a solution for both equations, it is a solution of the system.

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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.

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**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 = 3 y + 2 = x y= x – 2 y= x – 1 Solve each equation for y.

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Example 2A Continued On the graph, the lines appear to intersect at the ordered pair (3, 1)

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**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.

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**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.

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**Example 3A: Classifying Linear System**

Classify the system and determine the number of solutions. x = 2y + 6 3x – 6y = 18 y = x – 3 The equations have the same slope and y-intercept and are graphed as the same line. Solve each equation for y. The system is consistent and dependent with infinitely many solutions.

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Homework Pg # 28,29,35,37,40,45

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