Infinitely Many Solutions
Explore systems of linear equations with infinitely many solutions in this Grade 8 math worksheet.
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Infinitely Many Solutions
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Read each question carefully and answer to the best of your ability. Show all your work for short answer questions.
1. Which of the following systems of equations has infinitely many solutions?
y = 2x + 1 y = 2x - 3
y = 3x + 2 y = -3x + 2
y = 4x - 5 2y = 8x - 10
x + y = 7 x - y = 3
2. When two linear equations have infinitely many solutions, their graphs are:
Parallel lines
Intersecting lines
The same line
Perpendicular lines
3. A system of equations with infinitely many solutions means that the equations are .
4. If you multiply one equation in a system by a constant and get the other equation, the system has solutions.
5. Determine if the following system of equations has infinitely many solutions. Explain your reasoning.
Equation 1: 3x + 2y = 6
Equation 2: 6x + 4y = 12
6. A system of two linear equations can have exactly two solutions.
True
False
7. If two lines have the same slope and different y-intercepts, they have infinitely many solutions.
True
False
8. Graph the following system of equations on the coordinate plane below and determine if it has infinitely many solutions:
Equation 1: y = x + 2
Equation 2: 2y = 2x + 4