Substitution With No or Infinitely Many Solutions
Written by Adi Ackerman, Head Teacher
"Substitution With No or Infinitely Many Solutions" is written for 8th Grade (Ages 13-14), and it covers Common Core 8.EE.C.8.B. A 7th grader who is already steady on systems of equations can use it too, and an older student can use it as a short review.
8th grade math worksheet: substitute in eight systems such as y = 2x + 1 and 6x minus 3y = 4, then circle One, None or Many. Answer key included. Part of our number of solutions of systems collection. Aligned to Common Core standards.
How do I use this worksheet?
Begin with the graphing sheet so students see parallel and matching lines. Then use the substitution sheet and finish with the equations sheet, which needs no graphing.
What students will practice
- Students will solve systems by substitution and simplify.
- Students will recognize a false statement as no solution and a true one as many solutions.
- Students will write the ordered pair when a system has one solution.
Solve Systems by Graphing, Slope-Intercept Pairs
Graph Systems Given in Standard Form
Graph Systems With Horizontal and Vertical Lines
Graph Systems With Fraction Slopes
Read System Solutions From Graphs
Read Solutions From Graphs and Write the System
Estimate Graph Solutions, Then Solve Exactly
Treasure Map Systems, Locate the Hidden Points
Curriculum Links
Common Core State Standards
Expressions and Equations · 8th Grade
Standard: Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection.
View all 8.EE.C.8.B worksheets →Find this in the curriculum
Browse the grade, subject, and topic this belongs to.
FAQ
How do I use this number of solutions of systems worksheet?
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Begin with the graphing sheet so students see parallel and matching lines. Then use the substitution sheet and finish with the equations sheet, which needs no graphing.
What does this worksheet teach?
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Substitute in eight systems such as y = 2x + 1 and 6x minus 3y = 4, then circle One, None or Many. The directions on the page read: Substitute and simplify. Circle One, None or Many (infinitely many) solutions. If there is one solution, write the pair. An answer key is included.
Can I use this number of solutions of systems worksheet for homeschool or classroom?
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Yes, both. We made it for 8th grade systems of equations, and it works the same at home or at school. At home, a student can work through it alone and then go over it with you, which shows quickly what is solid and what needs another look. In class it works as independent practice, homework or a warm-up, and you can print one copy or a full set.
How can you tell how many solutions a system has without solving it?
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Write both equations as y = mx + b. Different slopes mean one solution. The same slope with different y-intercepts means no solution, and the same slope and y-intercept means infinitely many.
What happens when you substitute in a system with no solution?
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The variables cancel and you are left with a false statement, such as 0 = 5. A true statement, such as 4 = 4, means infinitely many solutions. Substitution With No or Infinitely Many Solutions practices both.
What does a system with infinitely many solutions look like on a graph?
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Both equations make the same line, so the two graphs lie on top of each other and share every point. Graph Systems, Parallel and Same Line Cases includes pairs like y = negative x + 4 and 2x + 2y = 8.
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Worksheet Details
| Grade | 8th Grade |
| Subject | Math |
| Topic | Systems of Equations |
| Standard | 8.EE.C.8.B |
| Pages | 1 page |
| Difficulty | Medium |
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Solve Systems by Graphing, Slope-Intercept Pairs
Graph Systems Given in Standard Form
Graph Systems With Horizontal and Vertical Lines
Graph Systems With Fraction Slopes
Read System Solutions From Graphs
Read Solutions From Graphs and Write the System
Estimate Graph Solutions, Then Solve Exactly
Treasure Map Systems, Locate the Hidden Points