7.5 Systems: Recognizing 0, 1 or Infinitely Many Solutions

7.5 Identifying the # of Solutions for Special Systems of Equations

Take Notes from Slides (there are 2) & check understanding with each set of questions.

TAKE NOTES FROM THIS SLIDE

Multiple Choice

How many solutions will this system have?

• No solution

• One Solution

• I Don't Know

• Infinitely Many Solutions

Multiple Choice

Which graph represents a system of equations with ONE solution?

• None of the above

Multiple Choice

If a system of linear equations has infinitely many solutions, what does this mean about the two lines?

• Intersecting lines

• Same line (overlapping)

• Parallel lines

Infinite Solutions & No Solutions

*How you will know when solving (without a graph)*

Sometimes when solving using substitution and elimination, we are left with "weird" equations

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• If an equations variables cancel out but what is left is "true" we say that it has infinite solutions.

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• If an equations variables cancel but what is left is "false" we say that is has no solutions.

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*Note: do not follow this rule when CHECKING solutions. Just when solving.​

Read & Then summarize in notes

Multiple Select

You solve a system of equations and you last line is:

4 = -5

What does this mean? (2 choices can be selected)

• There is no solution.

• The lines are parallel.

• The lines intersect.

• The solution is (4, -5)

• The are infinite solutions.

Multiple Select

You solve a system of equations and you last line is:

x = 5

What does this mean? (2 choices)

• The graph of the lines intersect at one point

• There is one solution.

• The are infinitely many solutions.

• There is no solution.

• The graph is of parallel lines

Multiple Choice

When solving a system of equations algebraically, which statement results in infinite solutions?

• 4 = 7

• 2 = 2

• -3 = 3

• all of the above

Multiple Choice

Solve the system of equations.

• (3, 33)

• (7, 77)

• (2, 22)

• No solution

• Infinite solutions

Multiple Choice

Solve the system of equations.

• (-6, 1)

• (0, 0)

• (1, -6)

• No solution

• Infinite solutions

Multiple Choice

y = 3x + 2
y - 3x = 2

• no solution
• infinite solutions
• (0 , 0)
• (2 , 2)

Poll

You have completed this lesson. You next steps to apply what you have learned would include continuing DeltaMath for Ch4. Before you leave this presentation, rate you confidence in identifying how many solutions a system has...

• 1 - I still don't really understand this lesson

• 2 - I wasn't sure how to answer questions but once I saw the answers, they made sense.

• 3 - I feel that I could explain how to recognize if a system of equations had 0 or infinitely many solutions