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7.1 Systems of Linear Equations

7.1 Systems of Linear Equations. Graphing Method. Reminders Write each equation in slope-intercept form Graph each line on the coordinate plane Label your lines Identify the solution for the system. Systems of Equations – 2 Variables. Solve each system by graphing. Substitution Method.

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7.1 Systems of Linear Equations

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  1. 7.1 Systems of Linear Equations

  2. Graphing Method • Reminders • Write each equation in slope-intercept form • Graph each line on the coordinate plane • Label your lines • Identify the solution for the system

  3. Systems of Equations – 2 Variables

  4. Solve each system by graphing

  5. Substitution Method • Reminders – 2 Equations • Solve either equation for one variable in terms of the other • Substitute for that variable into the other equation and solve • Substitute your answer into either of the original equations to find the value of the other variable

  6. Possible solutions for a system of equations with 2 variables

  7. Solve each system of equations using the Substitution Method

  8. Elimination Method • Reminders – 2 Equations • Eliminate either variable • Find the additive inverse of one variable by multiplying either/both equations by a constant • Add the two equations vertically • Solve for one variable and substitute the value of the variable into either of the original equations

  9. Solve each system of equations using the Elimination Method

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

  11. Solve each system of equations with three variables

  12. Linear Word Problems • Reminders • Identify your variables • Set up a table when appropriate • Set up a system of equations and solve • Write the solution to the system in a sentence answering the given question

  13. The perimeter of a rectangular floor is 208 feet. Find the dimensions of the floor if the length is three times the width.

  14. Four cheeseburgers and two chocolate shakes cost a total of $20.40. Two shakes cost $1.20 more than two cheeseburgers. What is the cost of a cheeseburger? What is the cost of a chocolate shake?

  15. With a tail wind, a small Piper aircraft can fly 2400 miles in 10 hours. Against this same wind, the Piper can fly the same distance in 12 hours. Find the average wind speed and the average air speed of the Piper.

  16. 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?

  17. 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?

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