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. Methods of Solving 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. Solving by Substitution
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

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 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

14. One Step Further
Word Problems

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