Question

Consider the two equations 4x+22=8x+10, 3x+18=5x+8 form a system with one solution. Solve the equations.

Answer 1

To determine whether the system of equations has one solution, we need to determine if the two lines intersect at a single point. In order to do this, we need to solve the system of equations simultaneously.

Let's solve the first equation 4x + 22 = 8x + 10:
- Subtract 4x from both sides: 22 = 4x + 10
- Subtract 10 from both sides: 12 = 4x
- Divide both sides by 4: x = 3

Now let's solve the second equation 3x + 18 = 5x + 8:
- Subtract 3x from both sides: 18 = 2x + 8
- Subtract 8 from both sides: 10 = 2x
- Divide both sides by 2: x = 5

Since the values of x are different in both equations (3 and 5), the system does not have one solution. Therefore, the system is inconsistent.