Question

\(x+y+n=15\)
\(x+y+k=9\)

Column A	Column B
\(n-k\)	6

 

Hint:

Another quick method is to subtract the second equation from the first: \((x+y+n) - (x+y+k) = 15 - 9\). The \(x\) and \(y\) terms cancel out, leaving \(n-k = 6\).

Answer 1

Step 1: Understanding the Concept:
This problem involves a system of two linear equations with four variables. We need to manipulate these equations to find the value of the expression in Column A.
Step 2: Key Formula or Approach:
The key is to notice the common term \(x+y\) in both equations. We can isolate this term in each equation and then set the results equal to each other. This will give us an equation with only \(n\) and \(k\).
Step 3: Detailed Explanation:
We are given the two equations:
1) \(x+y+n=15\)
2) \(x+y+k=9\)
From equation (1), we can isolate the term \(x+y\):
\[ x+y = 15 - n \] From equation (2), we can also isolate the term \(x+y\):
\[ x+y = 9 - k \] Since both expressions are equal to \(x+y\), we can set them equal to each other:
\[ 15 - n = 9 - k \] The question asks for the value of \(n-k\). Let's rearrange the equation to solve for this expression. Add \(n\) to both sides:
\[ 15 = 9 - k + n \] Subtract 9 from both sides:
\[ 15 - 9 = n - k \] \[ 6 = n - k \] The value of the expression in Column A is exactly 6.
Step 4: Final Answer:
The value of Column A is 6, which is equal to the value in Column B.