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Solving a System of Equations

Solving a System of Equations. Linear and Linear Inequalities. A set of two or more equations in two or more variables Linear system- variables in each equation are all to the power of one

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Solving a System of Equations

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  1. Solving a System of Equations Linear and Linear Inequalities

  2. A set of two or more equations in two or more variables • Linear system- variables in each equation are all to the power of one • Inequality- the equal sign has been replaced with less than, less than or equal to, greater than, or greater than or equal to What is a system?

  3. A set of values that satisfy all the equations in the system. Solution Set

  4. 3 Methods • Solving by substitution- solve one equation for a variable and plug into the other • Solving by elimination- adding or subtracting one equation from the other • Graphing- graphing both equations and looking for intersection points Methods of Solving

  5. Three possibilities for the number of solutions in a two equation system with two different variables • No solution • One solution • Infinitely many solutions Linear Systems

  6. 1. Solve one equation for x or y. • 2. Substitute the expression for x or y into the other equation • 3. Solve for the remaining variable • 4. Substitute the value found in Step 3 into one of the original equations, and solve for the other variable • 5. Verify the solution in each equation Solving by Substitution

  7. 1. Multiply one or both of the equations by a nonzero constant so that the coefficients of x or y are opposites of one another • 2. Eliminate x or y by adding the equations, and solve for the remaining variable • 3. Substitute the value found in step 2 into one of the original equations and solve for the other variable • 4. Verify the solution in each equation Solving by Elimination

  8. One Step Further Word Problems

  9. Read the problem • Define variables • Write out the two equations first • Solve using substitution, graphing, or elimination Linear System Word Problems

  10. A ball game is attended by 575 people and total ticket sales are $2575. If tickets cost $5 for adults and $3 for children, how many adults and how many children attended the game

  11. A café sells two kinds of coffee in bulk. The Costa Rican sells for $4.50 per pound and the Kenyan sells for $7.00 per pound. The owner wishes to mix a blend that would sell for $5.00 per pound. How much of each type of coffee should be used in the blend?

  12. A toy company makes dolls, as well as collector cases for each doll. To make x cases costs the company $5000 in fixed overhead, plus $7.50 per case. An outside supplier has offered to produce any desired volume of cases for $8.20 per case. • Write an equation that expresses the company’s cost to make x cases • Write an equation that expresses the cost of buying x cases from the outside supplier • When should the company make cases themselves, and when should they buy them from the outside supplier?

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