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Solving a system of equations by substitution WARM UP

Solving a system of equations by substitution WARM UP. SOLVE THE SYSTEM OF EQUATIONS Y = -2X + 7 Y = X + 1 Y = - 2 X + 7 1 = Y – X. systems. What kind of solutions do systems of equations have? What kind of solutions do parallel lines have? What kind of solutions do the same line have?.

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Solving a system of equations by substitution WARM UP

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  1. Solving a system of equations by substitution WARM UP SOLVE THE SYSTEM OF EQUATIONS Y = -2X + 7 Y = X + 1 Y = -2X + 7 1 = Y – X

  2. systems • What kind of solutions do systems of equations have? • What kind of solutions do parallel lines have? • What kind of solutions do the same line have?

  3. Solve using graphing • y = x + 3 • y = -x + 7

  4. Solve using graphing • 2y + 2x = 6 • 3y - 3x = 3

  5. Method for substitution • Choose one equation and solve for x or y. • Substitute the expression from that equation into the other equation and solve. • Substitute the value found in step 2 back into the equation solved in step one.

  6. Solve using substitution • 4x – 2y = -6 • X + 3y = 9

  7. Solve using substitution • 2x + y = 0 • 5x – 4y = 26

  8. Solving systems by elimination • Add the equations, eliminating one variable. Then solve the equation. • Substitute to solve for the other variable. • -6x – 4y = -10 • 6x + 2y = 8

  9. Solve the system using elimination • -x - 2y = 0 • -6x + 2y = 14

  10. Solve the system using elimination • 3X – 3y = 9 • -4x + 3y = 12

  11. Solve the system using elimination • X – 5y = 2 • 3x + 5y = 6

  12. Solve the system using elimination • X – y = 7 • 6x + y = 7

  13. Solving systems by elimination • What happens if the equations aren’t written in a way that something can easily be added to zero? • NEW STEPS! • Choose which variable to eliminate x or y • Decide what to multiply by so that when you add the desired variable eliminates. • Add the two equations together • Solve for the remaining variable • Substitute back in to one of the original equations to solve for other variable.

  14. What would you do to solve a system like this? • 3x + 2y = -6 • 2x + 5y = 7

  15. Solve using elimination 6x + 2y = 2 -3x + 3y = -9

  16. Solve using elimination 2x - 3y = 4 -4x + 5y = -8

  17. Solve using elimination -2x = 2y - 4 -7x + 6y = 25

  18. Solve using elimination 3x + 2y = 8 2y = 12 – 5x

  19. Solve using elimination -16x + 3y = -19 -8x – y = -7

  20. Solve using elimination -3x – 8y = 24 -4x – 5y = -2

  21. Which Method To Use? • For each of the systems of equations shown, choose which method would be the best option to use in solving the system: • Substitution Method • Elimination Method • Graphical Method

  22. Break even points • A car company spends $8,900 to make each new car. The company charges $12,900 for each new car. The company also spent $60,000,000 on building the new car plant. How many cars need to be sold to pay for the new plant?

  23. Word problem strategies • Define variables - what in the problem don’t you know? • Define what you are looking for – what is the problem asking you to find? • Define equations – what information in the problem can go together in an equation?

  24. Tyler is catering a banquet for 250 people. Each person will be served either a chicken dish that costs $5 each or a beef dish that costs $7 each. Tyler spent $1500. How many dishes of each type did Tyler serve?

  25. more word problems • The perimeter of a rectangle is 66 cm and its width is half its length. What are the length and width of the rectangle?

  26. Which job? • There are two different jobs Jordan is considering. The first job will pay $4200 per month plus an annual bonus of $4500. The second job pays $4100 per month plus $600 per month toward her rent and an annual bonus of $500. Which job should she take?

  27. Word problem • Two numbers added together is 7 • The difference of the two numbers is 1

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