Question

4x+22=8x+10 5x+5=5x+4

Plug a few points into the original equations and check to show that they can have no
solution. Explain your work.

Answer 1

4x+22=8x+10
We'll first solve for x by isolating it on one side:
4x - 8x = 10 - 22
-4x = -12
x = -12 / -4
x = 3

Now we'll plug x = 3 back into one of the original equations to check for a potential solution:
4(3) + 22 = 8(3) + 10
12 + 22 = 24 + 10
34 = 34

The first equation checks out, so let's move on to the second equation:

5x+5=5x+4
5(3) + 5 = 5(3) + 4
15 + 5 = 15 + 4
20 = 19

The second equation does not check out. Therefore, the system of equations has no solution, because the two equations contradict each other for the same value of x. This means that even though the first equation is satisfied by the value of x we found, the second equation cannot be satisfied by the same value.