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