Plug a few points into the original equations and check to show that they system of equations has one solution. The equations are 4x + 22 = 8x + 10 and 3x + 18 = 5x + 8
Let's plug in x = 3 into the first equation:
4(3) + 22 = 8(3) + 10
12 + 22 = 24 + 10
34 = 34
This shows that x = 3 satisfies the first equation.
Now, let's plug in x = 3 into the second equation:
3(3) + 18 = 5(3) + 8
9 + 18 = 15 + 8
27 = 23
This shows that x = 3 does not satisfy the second equation.
Since x = 3 does not satisfy both equations simultaneously, the system of equations does not have one solution.