How many solutions exist for the given equation? 3x + 13 = 3(x + 6) + 1 

Solution:

A system of linear equations has either:

1. No solution, or
2. Exactly one solution or,
3. Infinitely many solutions

A system of linear equations is said to be consistent if it has either one solution or infinitely many solutions; a system is inconsistent if it has no solution.

The stated problem contains the equation 3x + 13 = 3(x + 6) + 1is being rearranged below to get:

3x + 13 = 3(x + 6) + 1 --- (1)

3x + 13 = 3x + 18 + 1 --- (2)

13 = 18 + 1 --- (3)

Since variable x terms of the equation (2) cancels leaving us with equation (3) which makes no sense and hence is inconsistent.

Therefore it has no solution.

How many solutions exist for the given equation? 3x + 13 = 3(x + 6) + 1

Summary:

The equation 3x + 13 = 3(x + 6) + 1 is inconsistent and therefore has no solution.