# 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.

Math worksheets and

visual curriculum

visual curriculum