📘 Question
Find \(x\) and \(y\) such that:
\[
\begin{bmatrix}
3x + 7 & 5 \\
y + 1 & 2 – 3x
\end{bmatrix}
=
\begin{bmatrix}
0 & y – 2 \\
8 & 4
\end{bmatrix}
\]
✏️ Step-by-Step Solution
Step 1: Compare corresponding elements
- \(3x + 7 = 0\)
- \(5 = y – 2\)
- \(y + 1 = 8\)
- \(2 – 3x = 4\)
Step 2: Solve equations
From \(3x + 7 = 0\):
\[
x = -\frac{7}{3}
\]
From \(2 – 3x = 4\):
\[
-3x = 2 \Rightarrow x = -\frac{2}{3}
\]
❌ Contradiction → No common \(x\)
From \(5 = y – 2\):
\[
y = 7
\]
From \(y + 1 = 8\):
\[
y = 7
\]
✔ \(y\) is consistent, but \(x\) is not.
—
Step 3: Conclusion
Since values of \(x\) are inconsistent, the matrices cannot be equal.
✅ Final Answer
\[
\boxed{\text{No solution (matrices cannot be equal)}}
\]
💡 Key Concept
For matrices to be equal, all corresponding elements must match consistently.