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Solving Systems of Equations

Solving Systems of Equations. 4.2 Solving a System of Equations Using the Substitution Method. Solve one of the equations for either variable. Substitute this expression for the variable in the other equation. Solve this equation.

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Solving Systems of Equations

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  1. Solving Systems of Equations

  2. 4.2 Solving a System of Equations Using the Substitution Method • Solve one of the equations for either variable. • Substitute this expression for the variable in the other equation. • Solve this equation. • Substitute this value for the variable into the equation from step 1. • Write the solution as an ordered pair. • Check your solution.

  3. Solving a System of Equations Using the Substitution Method Solve:

  4. Solving a System of Equations Using the Substitution Method Solve:

  5. Solving a System of Equations Using the Substitution Method Dependent System: Solve:

  6. 4.3 Solving a System of Equations Using the Addition Method 1. Write each equation in standard form 2. Multiply one or both equations by the appropriate constant(s). 3. Add the two equations together. 4. Solve the resulting equation. 5. Substitute this value for the appropriate variable in either of the original equations, and solve for that variable. 6. Write the solution as an ordered pair. 7. Check your solution.

  7. Solving a System of Equations Using the Addition Method Solve:

  8. Solving a System of Equations Using the Addition Method Solve:

  9. Solving a System of Equations Using the Addition Method Solve: No Solution System:

  10. 4.4 Solving Applied Problems Using a System of Equations • Choose a variable for each unknown quantity. • Find two equations that relate the two unknown quantities. • Solve the system using substitution or addition.

  11. Solving Applied Problems Using a System of Equations (part 1) Adults are charged $6 to see a play, and children are charged $4. Last night 103 people saw a play, paying a total of $532. How many adults and how many children were at the play? Unknowns Number of adults: A, Number of Children: C System of Equations

  12. Solving Applied Problems Using a System of Equations (part 2) Solve by Addition There were 60 adults and 43 children at the play.

  13. Solving Applied Problems Using a System of Equations (part 1) The length of a rectangle is 3 inches more than twice its width. If the perimeter of the rectangle is 96 inches, find its length and width. Unknowns Length: L, Width: W System of Equations

  14. Solving Applied Problems Using a System of Equations (part 2) Solve by Substitution The length is 33 inches and the width is 15 inches.

  15. Solving Applied Problems Using a System of Equations (part 1) Manny deposited a total of $4000 in two bank accounts. One account paid 3% annual interest, and the other paid 4% annual interest. If Manny earned $145 interest in one year, how much was invested in each account? Unknowns Principal at 3%: x, Principal at 4%: y System of Equations

  16. Solving Applied Problems Using a System of Equations (part 2) Solve by Addition Manny invested $1500 at 3% and $2500 at 4%.

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