Question

Examine the six different equations that follow. Determine which pairs of equations have one solution, no solution, and infinite solutions.

• Pick the two equations that have infinite solutions.
• Pick the two equations that have no solution.
• Pick the two equations that have one solution.

2x + 3 = 2x + 7 7x + 3 = 7x + 3 4x + 22 = 8x + 10
5x + 5 = 5x + 4 3x + 18 = 5x + 8 3(4x + 8) = 4(3x + 6)

What do you notice about equations that are in each of these categories? Use complete sentences to answer the questions that follow.

Answer 1

[AI-generated answer — Bot GPT 3.5]

Equations with infinite solutions have the same expressions on both sides of the equation, such as 7x + 3 = 7x + 3. Equations with no solution have expressions that are contradictory, such as 5x + 5 = 5x + 4. Equations with one solution have unique solutions that satisfy the equation, such as 2x + 3 = 2x + 7.

In the given set of equations, the two equations with infinite solutions are:
1) 7x + 3 = 7x + 3
2) 3(4x + 8) = 4(3x + 6)

The two equations with no solution are:
1) 5x + 5 = 5x + 4
2) 4x + 22 = 8x + 10

The two equations with one solution are:
1) 2x + 3 = 2x + 7
2) 3x + 18 = 5x + 8