Copy and convert the following standard form equation into slope intercept form: 3x – 5y = 15 Write the slope and the y-intercept.

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Presentation transcript:

Copy and convert the following standard form equation into slope intercept form: 3x – 5y = 15 Write the slope and the y-intercept.

Solve systems of equations by using graphs and tables. Classify systems of equations, and determine the number of solutions. Objectives Essential Question How do you determine the number of solutions a system has?

 System of Equations: A set of two or more equations containing two or more variables.  Linear System: A system of equations containing only linear equations. lines that cross or the same line  Consistent System: A system of equations or inequalities that has at least ONE solution * lines that cross or the same line! parallel linesSame slope  Inconsistent System: A system of equations or inequalities that has NO solutions * parallel lines!! Same slope!!

equations are the same  Dependent System: A system of equations that has infinitely many solutions. *equations are the same  Independent System: A system of equations that has exactly one solution.  Examples for systems of equations Examples for systems of equations

1. Use substitution to determine if (3,3) is a solution to 2x – y = 3 y + x = 6 Yes

2. Use a graph to solve: y + x = 5 3x – 5y = -1 Slope intercept

Classify the following system as consistent, inconsistent, dependent or independent 2x – 3y = -15 3y – 2x = 15 This is a consistent and dependent system.

City Park Golf Course charges $20 to rent golf clubs plus $55 per hour for golf cart rental. Sea Vista Golf Course charges $35 to rent clubs plus $45 per hour to rent a cart. For what number of hours is the cost of renting clubs and a cart the same for each course? Practice: Summer Sports Application

Continued Continued Let x represent the number of hours and y represent the total cost in dollars. City Park Golf Course: y = 55x + 20 Sea Vista Golf Course: y = 45x + 35 Because the slopes are different, the system is independent and has exactly one solution. Step 1 Write an equation for the cost of renting clubs and a cart at each golf course.

Step 2 Solve the system by using a table of values. xy xy y = 55x + 20y = 45x + 35 Use increments of to represent 30 min. When x =, the y- values are both The cost of renting clubs and renting a cart for hours is $ at either company. So the cost is the same at each golf course for hours. Continued