Number of Solutions in Algebra
Explore linear and quadratic equations to determine the number of solutions, including unique solutions, no solutions, and infinite solutions.
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Number of Solutions in Algebra
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Read each question carefully and determine the number of solutions for each equation or system of equations. Show your work where applicable.
1. How many solutions does the equation 3x + 5 = 2x + 5 have?
Zero solutions
One solution
Two solutions
Infinitely many solutions
2. Which of the following quadratic equations has exactly one real solution?
x² + 4 = 0
x² - 4 = 0
x² + 4x + 4 = 0
x² + x + 1 = 0
3. A linear equation in one variable will have solutions unless the variables cancel out and result in a true or false statement.
4. The discriminant of a quadratic equation (b² - 4ac) determines the number of real solutions. If the discriminant is zero, there is real solution.
5. A system of two parallel lines has no solutions.
True
False
6. A quadratic equation can have three real solutions.
True
False
7. Determine the number of solutions for the system of equations: y = 2x + 3 y = 2x - 1
8. Consider the equation x² + 5x + c = 0. What value of 'c' would result in exactly one real solution?
9. Graph the following system of equations and determine the number of solutions. y = x + 2 y = -x + 4
Number of solutions: