Question 1: Examine the six different equations that follow. Determine which pairs of equations have one solution, no solution, and infinite solutions.

Question

• Put a circle around the two equations that have infinite solutions.
• Put a square around the two equations that have no solution.
• Underline 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.
in the first category (2x + 3 = 2x + 7) have the same terms on both sides of the equation, which makes them unsolvable. The second category of equations (7x + 3 = 7x + 3) have identical terms on both sides of the equation, making them consistent and having infinite solutions. The third category of equations (4x + 22 = 8x + 10) have different terms on both sides of the equation, showing that they have one solution.
(Question two is the one that needs solved)
Question 2: Infinite Solutions
Consider the two equations you circled, with infinite solutions. Solve the equations.

What does it mean to have infinite solutions?

Answer 1

Having infinite solutions means that any value for the variable in the equation will make the equation true. In other words, there are an infinite number of values that can be substituted for the variable that will satisfy the equation.