Asked by jamalhunter778

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.
Answer
2x+3=2x+7
This simplifies to
3 = 7
NO solutions

7x+3=7x+3
This works for any old value of x, infinite number of solutions

4x+22=8x+10
4 x = 12
x = 3
Whew,finally one solution :)

5x+5=5x+4
oh my, 5 = 4?
No solution again

3x+18=5x+8
2 x = 10
x = 5
one solid solution

3(4x+8)=4(3x+6)
12 x + 24 = 12 x + 24
any old x :)

Answer
Consider the two equations you circled, which form a system with infinite solutions.
Solve the equations.
Answer
Consider the two equations you put a square around, which form a system with no
solution. Solve the equations.
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