plug 2 points into the original equations and check to show that they can have no solution. explain your work. 2x+3=2x+7, 5x+5=5x+4
1. For the equation 2x+3=2x+7:
Let's plug in x=0:
2(0)+3 = 2(0)+7
0+3 = 0+7
3 = 7
This is not true. Therefore, the equation has no solution.
2. For the equation 5x+5=5x+4:
Let's plug in x=0:
5(0)+5 = 5(0)+4
0+5 = 0+4
5 = 4
This is not true. Therefore, the equation has no solution.
In both cases, when we plug in x=0, we arrive at a statement that is not true. This shows that there is no value of x that can satisfy either equation, making them inconsistent and having no solution.