Number of Solutions in Systems of Equations
Explore the number of solutions (one, none, or infinitely many) for systems of linear and non-linear equations, including graphical and algebraic methods.
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Number of Solutions in Systems of Equations
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Read each question carefully and determine the number of solutions for each system of equations. Show all your work.
1. Which of the following systems of equations has infinitely many solutions?
y = 2x + 1 y = -2x + 1
y = 3x - 5 2y = 6x - 10
x + y = 7 x + y = 5
y = x + 4 y = -x + 4
2. A system of two linear equations has no solution if the lines are:
Intersecting
Coincident
Parallel and distinct
Perpendicular
3. A system of equations with exactly one solution is called a system.
4. If a system of equations has no solution, the graphs of the equations are lines.
5. Determine the number of solutions for the following system of equations algebraically: 2x + 3y = 12 4x + 6y = 24
6. Graph the following system of equations and determine the number of solutions: y = -x + 3 y = x + 1
Number of Solutions:
7. A system of two non-linear equations can have more than two solutions.
True
False
8. The system y = x² and y = x - 5 has exactly one solution.
True
False
Match the description with the correct number of solutions.
9. Parallel lines with different y-intercepts
a. One Solution
10. Two lines that intersect at a single point
b. No Solution
11. Two identical lines
c. Infinitely Many Solutions