Plug a few points into the original equations and check to show that the system of
equations has one solution. Explain your work.4x+22=8x+10 and 3x+18=5x+8
For the first equation, 4x+22=8x+10, we can choose x=3 as a test point to check if it satisfies the equation.
Plugging x=3 into the equation:
4(3) + 22 = 8(3) + 10
12 + 22 = 24 + 10
34 = 34
Therefore, x=3 is a valid solution for the first equation.
Next, for the second equation, 3x+18=5x+8, we can choose x=2 as a test point to check if it satisfies the equation.
Plugging x=2 into the equation:
3(2) + 18 = 5(2) + 8
6 + 18 = 10 + 8
24 = 18
Therefore, x=2 is NOT a valid solution for the second equation.
Since the system of equations has one solution, it must be the point that satisfies both equations. By plugging x=3 into the second equation as well, we confirm that it holds true for both equations. Thus, the system of equations has one solution: x=3.