# Graphing Linear Systems Worksheets

How to Graph Linear Systems - A system of linear equation comprises two or more linear equations. The solution of a linear system is the ordered pair that is a solution to all equations in the system. One way of solving a linear system is by graphing. The solution to the system will then be in the point in which the two equations intersect. It's a good idea to always check your graphical solution algebraically by substituting x and y in your equations with the ordered pair. A linear system that has exactly one solution is called a consistent independent system. Consistent means that the lines intersect and independent means that the lines are distinct. Linear systems compose of parallel lines that have the same slope but different y-intersect do not have a solution since the lines won't intersect. Linear systems without a solution are called inconsistent systems. Linear systems composed of lines that have the same slope and the y-intercept are said to be consistent dependent systems. Consistent dependent systems have infinitely many solutions since the lines coincide.

• ### Basic Lesson

Demonstrates how to graph linear systems when given three points. Practice problems are provided. Graph: y = x + 2 and y = 2x + 1 For both equations, assume values of x and find the value of y. Show all three points (x , y) on graph. Draw both lines.

• ### Intermediate Lesson

Explores how to graph linear systems with four lines. Practice problems are provided. The point of intersection of the two lines (1,-1) is the solution to the system of equations.

• ### Independent Practice 1

Solve the following system of equations graphically. The answers can be found below.

• ### Independent Practice 2

Features another 20 Graphing Linear Systems problems.

• ### Homework Worksheet

12 Graphing Linear Systems problems for students to work on at home. Example problems are provided and explained.

• ### Topic Quiz

10 Graphing Linear Systems problems. A math scoring matrix is included.

• ### Homework and Quiz Answer Key

Answers for the homework and quiz.

• ### Lesson and Practice Answer Key

Answers for both lessons and both practice sheets.

#### Fun Fact

In correspondence with Fermat, Blaise Pascal laid the foundation for the Theory of Probability.