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For each system of equations, drag the true statement about its solution set to the box under the system.

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For each system of equations, drag the true statement about its solution set to the box under the system.

One Solution:
The graphs of these lines would intersect at one point.

Infinitely Many Solutions:
Both the right and left sides of the equations are equivalent expressions.

Zero Solutions:
y is equal to two different expressions.

Zero Solutions:
2x + 4 = x + 4 has no solutions.

Infinitely Many Solutions:
2x + 4 is a multiple of x + 4.




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    1 Answer

    1. Quizzma Team

      To match the true statements to the correct systems of equations, let’s break down each option:

      1. One Solution:

      The graphs of these lines would intersect at one point.

      – This is true for a system with two lines that are not parallel; they intersect at a single point.

      2. Infinitely Many Solutions:

      Both the right and left sides of the equations are equivalent expressions.

      – This is true for a system where both equations represent the same line, meaning every point on the line is a solution.

      3. Zero Solutions:

      y is equal to two different expressions.

      – This is correct when the left-hand sides of two equations lead to a contradiction (like y = 2 and y = 3).

      4. Zero Solutions:

      2x + 4 = x + 4 has no solutions.

      – This statement is true because when you simplify it (subtracting x and 4 from both sides), you get x = 0 = x, which leads to a contradiction.

      5. Infinitely Many Solutions:

      2x + 4 is a multiple of x + 4.

      – This is true because you could express both equations in such a way that they represent the same line.

      So, the assignments would be:

      – One Solution: The graphs of these lines would intersect at one point.

      – Infinitely Many Solutions: Both the right and

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