Ask a New Question
Menu

Match the description of the variable equation with the number of solutions it will have.

ax + c1 = c squared

The number of x's on both sides of the equation is different a =/ b ___________
The number of x's is the same on both sides of the equation, and the constant if different a = b, c1 =/ c squared ____________
The number of c's is the same on both sides of the equation and the constant is also the same a = b, c1 = c squared
Options to fill in the blanks: No Solution, One Solution, Two Solutions, Three Solutions, Infinite Solutions

3 answers

Let's analyze the descriptions and match them with the potential number of solutions based on how the variables are structured.

  1. The number of x's on both sides of the equation is different (a ≠ b):

    • Since the number of x's (coefficients of x) is different, there won't be the same degree for x, leading to the conclusion that there can be either no solution or infinite solutions, depending on the specific values. However, generally, the equation would likely have No Solution if there is no way to satisfy the equation across all x's.

    Answer: No Solution

  2. The number of x's is the same on both sides of the equation, and the constant is different (a = b, c1 ≠ c squared):

    • If the x's are balanced in terms of their coefficients, but the constants are different, we will end up having a single linear equation that is contradictory. This typically leads to No Solution as there is no value of x that will satisfy both sides.

    Answer: No Solution

  3. The number of c's is the same on both sides of the equation and the constant is also the same (a = b, c1 = c squared):

    • When both the coefficients of x and the constants match on both sides, it leads to an identity, which generally means any value of x will satisfy the equation. Thus, this can result in Infinite Solutions.

    Answer: Infinite Solutions

So the final answers are:

  1. No Solution
  2. No Solution
  3. Infinite Solutions
can only have one answer at each blank

Thank you for the clarification! Let's match the descriptions with single answers for each blank based on common mathematical interpretations:

  1. The number of x's on both sides of the equation is different (a ≠ b):

    • Answer: No Solution

  2. The number of x's is the same on both sides of the equation, and the constant is different (a = b, c1 ≠ c squared):

    • Answer: No Solution

  3. The number of c's is the same on both sides of the equation and the constant is also the same (a = b, c1 = c squared):

    • Answer: Infinite Solutions

So filled in, the responses become:

  1. No Solution
  2. No Solution
  3. Infinite Solutions

If there's anything else, feel free to ask!