Question

Plug a few points into 4x+22=8x+10, 3x+18=5x+8 and check to show that the system of equations has one solution. Explain your work.

Answer 1

To check whether the system of equations has one solution, we need to substitute some values for x and check if it satisfies both equations.

Let's plug in x = 2 into the first equation 4x + 22 = 8x + 10:

4(2) + 22 = 8(2) + 10
8 + 22 = 16 + 10
30 = 26

Since 30 is not equal to 26, x = 2 does not satisfy the first equation.

Now, let's plug in x = 2 into the second equation 3x + 18 = 5x + 8:

3(2) + 18 = 5(2) + 8
6 + 18 = 10 + 8
24 = 18

Since 24 is not equal to 18, x = 2 does not satisfy the second equation.

Therefore, we can conclude that the system of equations does not have one solution based on the given values of x.