A system of equation is as shown below
`x + l = 6`
`x - m = 5`
`x + p = 4`
`x - q = 3`
What is the value of `l + m + p + q` ?

Options

A. 2
B. 3
C. 4
D. 5

Answer

To solve the system of equations given by:

1. \( x + l = 6 \) (Equation 1)
2. \( x - m = 5 \) (Equation 2)
3. \( x + p = 4 \) (Equation 3)
4. \( x - q = 3 \) (Equation 4)

we need to find the value of \( l + m + p + q \).

### Step-by-Step Solution:

**Step 1: Isolate the variables \( l, m, p, \) and \( q \)**

From Equation 1:
\[ l = 6 - x \]

From Equation 2:
\[ m = x - 5 \]

From Equation 3:
\[ p = 4 - x \]

From Equation 4:
\[ q = x - 3 \]

**Step 2: Substitute the expressions for \( l, m, p, \) and \( q \)**

Now we can express \( l + m + p + q \) in terms of \( x \):
\[ l + m + p + q = (6 - x) + (x - 5) + (4 - x) + (x - 3) \]

**Step 3: Simplify the expression**

Combine the terms:
\[ l + m + p + q = 6 - x + x - 5 + 4 - x + x - 3 \]

Notice that the \( -x \) and \( +x \) terms cancel out:
\[ l + m + p + q = 6 - 5 + 4 - 3 \]

Now, simplify the constants:
\[ l + m + p + q = 1 + 1 = 2 \]

### Final Answer:
Thus, the value of \( l + m + p + q \) is:
\[ \boxed{2} \]