Examine the six different equations that follow. Determine which pairs of equations have one solution, no solution, and infinite solutions. On your worksheet,
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+37x+34x+225x+53x+183(4x+8)======2x+77x+38x+105x+45x+84(3x+6)
To determine which pairs of equations have one solution, no solution, and infinite solutions, we need to simplify each pair of equations and then compare them.
First, let's simplify the equations:
Equation 1:
2x + 37x + 34x + 22
2x + 78x + 183x + 183
(4x + 8)
Equation 2:
2x + 7
7x + 3
8
(3x + 6)
Now, let's compare the simplified equations to determine the solutions:
Equation 1: 2x + 78x + 183 = 4x + 8
80x + 183 = 4x + 8
80x - 4x = 8 - 183
76x = -175
x = -175 / 76
Equation 2: 7x + 3 = 3x + 6
7x - 3x = 6 - 3
4x = 3
x = 3 / 4
Based on this analysis, we can determine the following:
- One solution: 7x + 3 = 3x + 6
- No solution: 2x + 78x + 183 = 4x + 8
- Infinite solutions: None
Therefore, based on the results, you should underline the equation 7x + 3 = 3x + 6 as having one solution, put a square around the equation 2x + 78x + 183 = 4x + 8 as having no solutions, and there are no equations with infinite solutions.