1. The equations [ 4x + 22 = 8x +10 ] and [ 5x + 5 = 5x +4 ] are the ones that form a system with no solution.
2. What stands out is that in both equations the variables cancel out completely, leaving contradictory statements such as 22 = 10 in the first equation and 5 = 4 in the second equation.
3. Having no solutions means that there is no possible value for the variables that will make both equations true simultaneously. In other words, the lines represented by the equations do not intersect and are parallel.
4. Let's plug in some points into the original equations:
- For the first equation [ 4x + 22 = 8x +10 ], if we choose x = 1, we get:
4(1) + 22 = 8(1) + 10
4 + 22 = 8 + 10
26 = 18 (which is false)
- For the second equation [ 5x + 5 = 5x + 4 ], if we choose x = 2, we get:
5(2) + 5 = 5(2) + 4
10 + 5 = 10 + 4
15 = 14 (which is false)
Therefore, the original system of equations has no solutions.
1 , Consider the [ 2x +3 = 2x + 7 , 4x + 22 = 8x +10 5x + 5 = 5x +4 ] equations you put a square around, which form a system with no solution.
2. What do you notice about these equations?
3. What does it mean to have no solutions?
4. Plug a few points into the original equations and check to show that they can have no
solution.
1 answer