Equations with No Solutions Worksheet
Explore linear equations and systems of equations that result in no solutions, focusing on parallel lines and contradictory statements.
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Equations with No Solutions
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Read each question carefully and follow the instructions to solve for the given variables. Pay close attention to equations that may not have a solution.
1. Which of the following equations has no solution?
3x + 5 = 2x + 10
4x - 7 = 4x + 2
5(x - 2) = 5x - 10
2x + 3 = x + 3
2. When graphing a system of two linear equations that has no solution, what will the graphs look like?
Intersecting lines
Coinciding lines
Parallel lines
Perpendicular lines
3. An equation has no solution if, after simplifying, the variables cancel out and you are left with a statement.
4. When solving a system of equations by substitution, if you arrive at a statement like 0 = 5, this indicates there is solution.
5. Determine if the following equation has one solution, no solution, or infinitely many solutions. Justify your answer. 4(x + 1) = 4x + 5
6. A system of linear equations with the same slope but different y-intercepts will always have no solution.
True
False
7. Consider the system of equations: Equation 1: y = 3x + 2 Equation 2: 6x - 2y = 4 Show algebraically why this system has no solution.
8. Graph the following system of equations and explain how the graph illustrates that there is no solution: y = 2x + 1 y = 2x - 3
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