Question

If x + y = 10 and x - y = 2, then y =

• A. 8
• B. 6
• C. 5
• D. 4
• E. 2

Hint:

For a system of equations in the form \(x+y=a\) and \(x-y=b\), you can quickly find \(y\) by calculating \(\frac{a-b}{2}\) and \(x\) by calculating \(\frac{a+b}{2}\). Here, \(y = \frac{10-2}{2} = 4\) and \(x = \frac{10+2}{2} = 6\).

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
We are given a system of two linear equations with two variables, \(x\) and \(y\). We need to solve for the value of \(y\).
Step 2: Key Formula or Approach:
We can use the elimination method to solve for \(y\). By subtracting one equation from the other, we can eliminate the variable \(x\).
Equation (1): \(x + y = 10\)
Equation (2): \(x - y = 2\)
Step 3: Detailed Explanation:
To find \(y\), we should eliminate \(x\). We can do this by subtracting Equation (2) from Equation (1):
\[ (x + y) - (x - y) = 10 - 2 \]
Distribute the negative sign:
\[ x + y - x + y = 8 \]
Combine the like terms:
\[ 2y = 8 \]
Divide by 2 to solve for \(y\):
\[ y = \frac{8}{2} = 4 \]
Step 4: Final Answer:
The value of \(y\) is 4, which corresponds to option (D).