Plug a few points into the original equations and check to show that the system of equations has one solution. Explain your work.

Question

5x+5=5x+4
3x+18=5x+4

Answer 1

For the first equation, let's plug in x = 1:

5(1) + 5 = 5(1) + 4
5 + 5 = 5 + 4
10 = 9

Since the equation is false, this particular x value does not satisfy the equation, indicating that there is only one solution.

Now, for the second equation, let's plug in x = 2:

3(2) + 18 = 5(2) + 4
6 + 18 = 10 + 4
24 = 14

Again, the equation is false when x = 2, proving that there is only one solution.