Number of Solutions in Algebra
Explore the number of solutions for linear equations, systems of linear equations, and quadratic equations.
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Number of Solutions in Algebra
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Date:
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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 = 3x - 2 have?
One solution
No solutions
Infinitely many solutions
Two solutions
2. For what value of 'k' will the equation 2x + 7 = kx + 7 have infinitely many solutions?
k = 0
k = 2
k = 7
k = -2
3. The system of equations y = 2x + 1 and y = 2x - 3 has no solutions.
True
False
4. If two lines intersect at exactly one point, the system of equations has infinitely many solutions.
True
False
5. A quadratic equation with a positive discriminant has real solutions.
6. If the graph of a quadratic equation does not intersect the x-axis, it has real solutions.
7. The equation x² + 4 = 0 has real solutions.
8. Graph the system of equations below and determine the number of solutions.
y = x + 2
y = -x + 4
Number of solutions:
Match each description with the correct number of solutions.
9. Parallel lines
a. One solution
10. Intersecting lines
b. No solutions
11. Coincident lines
c. Infinitely many solutions