Systems of Linear Equations

GRAPHING Method Reminders 1.Solve each equation for y 2.Graph each line on the coordinate plane using the slope and y-intercept 3.Label your lines

GRAPHING Method Inconsistent Consistent Independent Consistent Dependent

Substitution Method Reminders 1.Solve either equation for one variable in terms of the other 2.Substitute for that variable into the other equation and solve 3.Substitute into either one of the original equations to find the value of the other variable

Substitution Method Inconsistent Consistent Independent Consistent Dependent

Substitution Method

elimination Method Reminders 1.Eliminate either variable 2.Multiply either/both equations by some constant 3.Find the additive inverse of one variable and add the equations vertically 4.Solve for one variable 5.Substitute the value of the variable into either equation

Substitution Method Inconsistent Consistent Independent Consistent Dependent

elimination Method

Reminders 1.Pair any 2 equations and eliminate one variable 2.Pair any 2 other combination of equations and eliminate the same variable 3.Solve your new system for one variable 4.Substitute the value of the variable into either one of the previous equations and solve for the other variable 5.Plug the value of the 2 variables into either one of the original equations to find the third variable

elimination Method

Word Problems Reminders 1.Identify your variables 2.Set up a table when appropriate 3.Set up a system of equations 4.Solve the system for each variable 5. Write the solution to the system in a sentence

The perimeter of a rectangular floor is 90 feet. Find the dimensions of the floor if the length is twice the width.

Four large cheeseburgers and two chocolate shakes coast a total of $7.90. Two shakes cost $0.15 more than one cheeseburger. What is the cost of a cheeseburger? What is the cost of a chocolate shake?

With a tail wind, a small Piper aircraft can fly 600 miles in 3 hours. Against this same wind, the Piper can fly the same distance in 4 hours. Find the average wind speed and the average air speed of the Piper. RateTimeDistance With Wind Against Wind

A doctor’s prescription calls for a daily intake containing 40mg of vitamin C and 30mg of vitamin D. Your pharmacy stocks two compounds that can be used: one contains 20% vitamin C and 30% vitamin D, the other 40% vitamin C and 20% vitamin D. How many mgs of each compound should be mixed to fill the prescription?

A movie theater charges $8.00 for adults, $4.50 for children, and $6.00 for senior citizens. One day the theater sold 405 tickets and collected $2320 in receipts. There were twice as many children’s tickets sold as adult tickets. How many adults, children, and senior citizens went to the theater that day?

Solving Systems of Inequalities

GRAPHING Method Reminders 1.Graph each function and shade the graph appropriately 2.The solution is the area where the functions overlap 3.If the functions do not overlap then the system has no solution

The graph of a system of linear inequalities is said to be bounded, if it can be contained within some circle of sufficiently large radius. The graph of a system of linear inequalities is said to be unbounded, if it cannot be contained within a circle.

Bounded or Unbounded Name the corner points