Download Solving Systems of Linear Equations by Graphing Worksheet

Math 154 Elementary Algebra
Caspers
Name___________________________
Date____________________________
Solving Systems of Linear Equations by Graphing—5.1
Solve each system of linear equations by graphing. If the system has one solution, find it. If the system has no solution, state so. If
the system has an infinite number of solutions, state what these solutions are.
1.
y  2x  5
x  y  7
Description of the graph:
Characteristics of lines:
Type of system:
Answer:
2.
4x  2 y  8
3x  y  1
Description of the graph:
Characteristics of lines:
Type of system:
Answer:
Page 1 of 3
3.
y  4x   1
8x  2 y  6
Description of the graph:
Characteristics of lines:
Type of system:
Answer:
4.
 6x  4  2 y
2  y  3x
Description of the graph:
Characteristics of lines:
Type of system:
Answer:
Page 2 of 3
Summary of Systems
There are three types of systems of linear equations in two variables:
1.
Independent systems have two lines that cross at a single point. This single point is the one and only solution to
the system. These two lines have different slopes.
2.
Inconsistent systems have two parallel lines that never cross. There is no solution to this type of system. These
two lines have the same slope, but different y-intercepts.
3.
Dependent systems have two equations that represent the same line. All of the points on this line are solutions to
the system; this is an infinite number of solutions. These two equations have the same slope and the same yintercept; hence, they represent the same line.
Express each equation in slope-intercept form. Without graphing, state whether the system of equations has exactly one
solution, no solution, or an infinite number of solutions.
5.
x  y  6
x  y  6
6.
1
x  4
2
2y  x  8
7.
x  y  3
1
x  3y   6
2
8.
y 
x  y  2
2x  2 y   2
Page 3 of 3