Presentation on theme: "Solving a System of Equations"— Presentation transcript:
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 oneInequality- the equal sign has been replaced with less than, less than or equal to, greater than, or greater than or equal toWhat is a system?
3 A set of values that satisfy all the equations in the system. Solution Set
4 Methods of Solving 3 Methods Solving by substitution- solve one equation for a variable and plug into the otherSolving by elimination- adding or subtracting one equation from the otherGraphing- graphing both equations and looking for intersection pointsMethods of Solving
5 Three possibilities for the number of solutions in a two equation system with two different variablesNo solutionOne solutionInfinitely many solutionsLinear Systems
6 Solving by Substitution 1. Solve one equation for x or y.2. Substitute the expression for x or y into the other equation3. Solve for the remaining variable4. Substitute the value found in Step 3 into one of the original equations, and solve for the other variable5. Verify the solution in each equationSolving by Substitution
10 Solving by Elimination 1. Multiply one or both of the equations by a nonzero constant so that the coefficients of x or y are opposites of one another2. Eliminate x or y by adding the equations, and solve for the remaining variable3. Substitute the value found in step 2 into one of the original equations and solve for the other variable4. Verify the solution in each equationSolving by Elimination
15 Linear System Word Problems Read the problemDefine variablesWrite out the two equations firstSolve using substitution, graphing, or eliminationLinear System Word Problems
16 A ball game is attended by 575 people and total ticket sales are $2575 A ball game is attended by 575 people and total ticket sales are $ If tickets cost $5 for adults and $3 for children, how many adults and how many children attended the game
17 A café sells two kinds of coffee in bulk. The Costa Rican sells for $4 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?
18 A toy company makes dolls, as well as collector cases for each doll 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 casesWrite an equation that expresses the cost of buying x cases from the outside supplierWhen should the company make cases themselves, and when should they buy them from the outside supplier?