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**Solving a System of Equations**

Linear and Linear Inequalities

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**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?

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**A set of values that satisfy all the equations in the system.**

Solution Set

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**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

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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

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**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

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**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

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One Step Further Word Problems

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**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

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**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

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**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?

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**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?

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3-2 Solving Equations by Using Addition and Subtraction Objective: Students will be able to solve equations by using addition and subtraction.

3-2 Solving Equations by Using Addition and Subtraction Objective: Students will be able to solve equations by using addition and subtraction.

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