Equations with infinite solutions are ones where the variables can be eliminated, leading to a true statement. In this case, the equations 2x+3=2x+7 and 7x+3=7x+3 have infinite solutions because they simplify to 3=3 and 3=3, respectively.
Equations with no solution are ones where the variables can be eliminated, leading to a false statement. In this case, the equations 4x+22=8x+10 and 5x+5=5x+4 have no solution because they simplify to a false statement, such as 22=10 and 5=4, respectively.
Equations with one solution are ones where the variables cannot be eliminated and result in a unique value for the variable. In this case, the equations 3x+18=5x+8 and 3(4x+8)=4(3x+6) have one solution because they simplify to 3=5 and 12x+24=12x+24, respectively.
Overall, equations with infinite solutions typically involve identical expressions or variables that can be eliminated, equations with no solution involve contradictory expressions or variables that can be eliminated, and equations with one solution involve unique values for the variables that cannot be eliminated.
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.
3 answers
make it shorter please
Equations with infinite solutions have identical expressions, equations with no solution have contradictory expressions, and equations with one solution have unique values for the variables.
1 answer