Equations with Infinite and No Solutions
Explore linear equations that result in infinite solutions (identities) or no solutions (contradictions) at a Grade 12 level.
Includes
Standards
Topics
Equations with Infinite and No Solutions
Name:
Date:
Score:
Read each question carefully and solve for the variable. Determine if the equation has one solution, no solutions, or infinitely many solutions. Show all your work.
1. Which of the following equations has infinitely many solutions?
3x + 5 = 3x - 2
2(x + 4) = 2x + 8
5x - 10 = 2x + 5
x/2 + 3 = x/2 - 1
2. An equation that has no solution is called a/an:
Identity
Contradiction
Conditional equation
Linear equation
3. An equation like 4x + 7 = 4x + 7 is an because it has many solutions.
4. If an equation simplifies to a false statement, such as 0 = 5, then it has solutions.
5. Solve the following equation and classify it as having one solution, no solution, or infinitely many solutions: 6(x - 2) + 10 = 6x - 2
6. Solve the following equation and classify it: 3(2x + 1) - 5 = 6x - 2
7. Solve the following equation and classify it: 5x - (2x + 3) = 3x - 3
8. An equation that simplifies to 0 = 0 has no solution.
True
False
9. If an equation has the same variable terms on both sides but different constant terms, it will have one solution.
True
False
10. For what value of 'k' would the equation 2(3x + 4) = kx + 8 have infinitely many solutions?
11. For what value of 'm' would the equation 5x - 7 = mx + 3 have no solution?
Related Worksheets
Perfect Square Trinomials
This worksheet focuses on identifying, factoring, and constructing perfect square trinomials, essential skills for Grade 12 Algebra.
Grade 12 Algebra: Standard Form
A Grade 12 math worksheet focusing on converting between different forms of linear equations, identifying slopes and intercepts, and graphing linear equations in standard form.
Characteristics of Parabolas Worksheet
Explore and identify the key characteristics of parabolas, including vertex, focus, directrix, and axis of symmetry.
Solving Equations with Variables on Both Sides
This worksheet provides practice on solving linear equations where variables appear on both sides of the equals sign.
Evaluating Algebraic Expressions
This worksheet focuses on evaluating complex algebraic expressions involving various operations and functions, suitable for Grade 12 students.
Graphing Parabolas Worksheet
A Grade 12 math worksheet on graphing parabolas, covering standard form, vertex form, and intercepts.
Grade 12 Sigma Notation Worksheet
A comprehensive worksheet for Grade 12 students covering sigma notation, including evaluating sums, expanding series, and writing expressions in sigma notation.
Polynomial Operations Worksheet
Grade 12 Math worksheet focusing on addition, subtraction, multiplication, and division of polynomials, including factoring and remainder theorem applications.