📘 Question
If
\[
\begin{bmatrix}
2x + y & 4x \\
5x – 7 & 4x
\end{bmatrix}
=
\begin{bmatrix}
7 & 7y – 13 \\
y & x + 6
\end{bmatrix}
\]
Find \(x + y\).
✏️ Step-by-Step Solution
Step 1: Compare corresponding elements
- \(2x + y = 7\)
- \(4x = 7y – 13\)
- \(5x – 7 = y\)
- \(4x = x + 6\)
Step 2: Solve for \(x\)
\[
4x = x + 6 \Rightarrow 3x = 6 \Rightarrow x = 2
\]
—
Step 3: Find \(y\)
\[
y = 5x – 7 = 5(2) – 7 = 3
\]
—
Step 4: Verify (optional)
✔ All equations satisfied —Step 5: Find \(x + y\)
\[
x + y = 2 + 3 = 5
\]
—
✅ Final Answer
\[
\boxed{5}
\]
—
💡 Key Concept
For matrix equality, corresponding elements must be equal. Solve systematically for consistent values.