Drill # 95 Graph the following linear equations (on the same graph)

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Drill # 95 Graph the following linear equations (on the same graph) 1. y = x + 2 2. y = x + 4 3. y = -x + 2

Launch Troy has 10 bills in his pocket, all 5’s and 10’s. If the total amount that he has adds up to $70, how many of each bill (5’s and 10’s) does he have? Write an equation that represents this situation…graph the equations…find the solution.

5-1 Graphing Systems of Equations Objective: To determine whether a system of equations has one, none, or infinitely many solutions. OPEN BOOKS to page 253

(1.) Systems of Equations** Definition: A set of equations with the same variables. Example: x + y = 2 3x – 2y = 6 How many solutions does this system have? What is a solution to system of equations?

(2.) Consistent and (3.) Inconsistent** Consistent: A system of equations that has at least one ordered pair that satisfies both equations. (consistent means there is a solution) Inconsistent: A system of equations that has no ordered pair that satisfies both equations. (inconsistent means no solution)

(4.)Dependent and (5.) Independent** Independent: A system that has exactly one solution. Dependent: A system of equations that has infinitely many solutions. All consistent systems of equations are either dependent (infinitely many solutions) or independent (one solution)

Possible solutions for systems of Equations* Graphs of Equations Number of Solutions Terminology Intersecting lines Exactly one consistent and independent Same line Infinitely many consistent and dependent Parallel lines None inconsistent

Number of Solutions* If a system has one solution, name it. Example 1 a,b: page 254 Check your progress: page 254 Study Guide: #1-#4

Graphing Linear Equations* Slope Intercept Form: y = mx + b 1. Plot the y-intercept (b) 2. Use the slope (rise/run) to find a second point 3. Draw a line through the points Standard Form: Ax + By = C 1. Find the x and y intercepts (sub y=0 to find x-intercept, x=0 to find y-intercept) 2. Draw a line through the points

To solve a system of equations* (by graphing) 1. Graph both equations on the same coordinate plane. 2. Determine solution: If they are parallel (same slope): no solution If they are the same line (same slope and y- intercept): infinitely many solutions If they intersect at one point: one solution