Infinite solutions:
3x+18=5x+8
3(4x+8)=4(3x+6)
1.Consider the two equations you circled, which form a system with infinite solutions?
2.Solve the equations.
3.What do you notice about these equations?
4.What does it mean to have infinite solutions?
5.Plug more than one point into the original equations and check to show that the equations can have more than one solution.
6.Explain your work.
1. The second equation, 3(4x+8)=4(3x+6), forms a system with infinite solutions.
2. Let's solve the second equation:
Simplify both sides:
12x + 24 = 12x + 24
Subtract 12x from both sides:
24 = 24
3. What stands out about these equations is that they simplify to a statement that is always true. This means that no matter what value x is assigned, the equations will always be equivalent.
4. Having infinite solutions means that there are an infinite number of values for x that satisfy the equations. In this case, any value of x will make the equations true.
5. Let's plug in some values for x into the original equations and check if they hold true:
For the first equation 3x + 18 = 5x + 8:
Let x = 0:
3(0) + 18 = 5(0) + 8
18 = 8 (false)
For the second equation 3(4x+8)=4(3x+6):
Let x = 1:
3(4*1+8) = 4(3*1+6)
3(12) = 4(9)
36 = 36 (true)
6. The fact that the equations simplify to a true statement means that they are equivalent for all values of x. This demonstrates that there are infinite solutions for these equations.