A system of linear equations allows the relationship between two or more linear equations to be compared and analyzed. 4.1 - Systems of Linear Equations.

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Presentation transcript:

A system of linear equations allows the relationship between two or more linear equations to be compared and analyzed Systems of Linear Equations in Two Variables

Determine whether (3, 9) is a solution of the following system. Both statements are true, therefore (3, 9) is a solution to the given system of linear equations Systems of Linear Equations in Two Variables

Determine whether (3, -2) is a solution of the following system. Both statements are not true, therefore (3, -2) is not a solution to the given system of linear equations Systems of Linear Equations in Two Variables

Solving Systems of Linear Equations by Graphing Systems of Linear Equations in Two Variables

Solving Systems of Linear Equations by Graphing Systems of Linear Equations in Two Variables

Solving Systems of Linear Equations by the Addition Method Systems of Linear Equations in Two Variables (Also referred to as the Elimination Method)

Solution Systems of Linear Equations in Two Variables Solving Systems of Linear Equations by the Addition Method (Also referred to as the Elimination Method)

Solution Systems of Linear Equations in Two Variables Solving Systems of Linear Equations by the Addition Method (Also referred to as the Elimination Method)

Solution Systems of Linear Equations in Two Variables Solving Systems of Linear Equations by the Addition Method (Also referred to as the Elimination Method)

True Statement Systems of Linear Equations in Two Variables Solution: All reals Lines are the same Solving Systems of Linear Equations by the Addition Method (Also referred to as the Elimination Method)

4.1 - Systems of Linear Equations in Two Variables lines are parallel False Statement No Solution Solving Systems of Linear Equations by the Addition Method (Also referred to as the Elimination Method)

Solving Systems of Linear Equations by Substitution Solution Systems of Linear Equations in Two Variables

Solving Systems of Linear Equations by Substitution Solution Systems of Linear Equations in Two Variables

Example Systems of Linear Equations in Two Variables LCD: 6 LCD: 15 Solution

A first number is seven greater than a second number. Twice the first number is four more than three times the second number. What are the numbers? Applications Substitution Method 1 st number is x, 2 nd number is y Solution

Two trains leave Tulsa, one traveling north and the other south. After four hours, they are 376 miles apart. If one train is traveling ten miles per hour faster than the other, what is the speed of each train? Substitution Method TrainRateTimeDistance North South x4 y 4x 4y Applications

A boat can travel 20 miles down-stream in 2 hours. It can travel 18 upstream in 3 hours. What is the speed of the boat in still water and the speed of the current? Elimination Method RateTimeDistance w/current Against curr Applications Boat speed: 8 mph Current speed: 2 mph Boat speed: x Current speed: y

One solution contains 20% acid and a second solution contains 50% acid. How many ounces of each solution should be mixed in order to have sixty ounces of a 30% solution? SolutionOuncesDecimalPure Acid 20% 50% 30% x 0.2 y 0.2x 0.5y (60)(0.3) Applications

One solution contains 20% acid and a second solutions contains 50% acid. How many ounces of each solution should be mixed in order to have sixty ounces of a 30% solution? Elimination Method Applications

For a particular show the price of an adult ticket is $2.00 and a child's ticket is $1.50. A total of 300 tickets were sold for $525. How many adult and children’s tickets were sold? TicketsTypePriceCost Adult Child Total A $2.00 C 2A 1.5C$ $ Applications 150 Adult tickets 150 Children’s tickets Elimination Method

The value of 12 coins is $1.20. The coin are nickels, dimes and quarters. The number of dimes is two more than twice the number of nickels. How many nickels, dimes and quarters are there? Elimination Method Applications nickels dimes quarter

4.4 – Systems of Linear Inequalities Graphing Inequalities in Two Variables Graph the solution.

Graphing Inequalities in Two Variables Graph the solution. 4.4 – Systems of Linear Inequalities

Graphing Inequalities in Two Variables Graph the solution. 4.4 – Systems of Linear Inequalities

Graphing Inequalities in Two Variables Graph the solution. 4.4 – Systems of Linear Inequalities

Graphing Inequalities in Two Variables Graph the solution. 4.4 – Systems of Linear Inequalities