Equations with Infinite and No Solutions
Explore linear equations that have either infinitely many solutions or no solutions through various problem types.
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Equations with Infinite and No Solutions
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Read each question carefully and follow the instructions. Determine if the given equations have one solution, no solution, or infinitely many solutions.
1. Which of the following equations has infinitely many solutions?
2x + 3 = 2x - 5
3x + 7 = 3x + 7
5x - 1 = 4x + 2
x + 10 = x - 10
2. Which of the following equations has no solution?
4x - 8 = 4x - 8
6x + 2 = 6x + 5
7x + 1 = x + 1
9x - 3 = 8x + 3
3. An equation with infinitely many solutions is also called an .
4. When solving an equation, if you arrive at a false statement (e.g., 0 = 5), the equation has .
5. Determine if the equation 4(x - 2) + 1 = 4x - 7 has one solution, no solution, or infinitely many solutions. Show your work.
6. For what value of 'a' would the equation ax + 5 = 3x + 5 have infinitely many solutions? Explain your reasoning.
7. The equation 7x - 3 = 7x + 3 has no solution.
True
False
8. An equation that simplifies to 0 = 0 has one unique solution.
True
False
9. Graph the system of equations below. What does the graph tell you about the number of solutions?
Equation 1: y = 2x + 1
Equation 2: 2y = 4x + 2
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