Systems of Linear Equations and Inequalities

Consist of two or more linear equations that have the same variables.

• Linear System

• Function Notation

• Direct Variation

• Literal Equation

An ordered pair that satisfies all of the equations in a linear system. The intersection point where the lines cross.

• Linear system

• Solution of a system of linear equations

• Elimination Method

• Substitution Method

A method used to solve systems of equations in which one variable is elimnated by adding or subtraction two equations of the system and solving for the variable.

• Elimination Method

• Substitutuion Method

• Graph of a system of Linear equations in two variables.

• Solution of a system of linear equations

A method used to solve systems of equations by solving an equation for one variable and substiutuing the resulting expression into the other euqation(s)

• Substiution Method

• Eliminations Method

• Graph of a system of Linear Inequalities in two variables

• Solution of a system of linear equaitons

Which system of equations is best represented by lines h and j?

• 
• 
• 
• 

A city bus collected $1,140 in fares on a given day. The regular fare is $1.50, and the reduced fare is $0.75. If 1,042 total fares were paid, which system of linear equations can be used to find x, the number of regular fares paid, and y, the number of reduced fares paid?

• A

• B

• C

• D

The two types of tickets sold at a baseball game are standard tickets and discounted tickets. The price of a discounted ticket was 80% of the price of a standard ticket. There were 153 standard tickets sold at the baseball game. There were 47 discounted tickets sold at the baseball game. The total amount of tickets sales from the standard and discounted tickets was $2,649.34. The line graphed on the grid represents the first equation in a system of linear equations for this situation. If the second equation in the system is y = 0.80x, what is the best estimate of the price of a discounted ticket?

• $13.95

• $14.55

• $13.25

• $11.15

If a system of linear equations has one solution, what does this mean about the two lines?

• Parallel lines

• the same line

• Intersecting lines

If a system of linear equations has infinitely many solutions, what does this mean about the two lines? 

• Intersecting lines

• Same line

• Parallel lines

If a system of equations has no solution, what does the graph look like?

• intersecting lines

• parallel lines

• coincident lines

• no lines