Question

If \(\begin{bmatrix} 4x & 5x-7 \\[0.3em] 4x & 2x+y\end{bmatrix}\)=\(\begin{bmatrix} x+6 & y \\[0.3em] 7y-13 & 7\end{bmatrix}\) then the value of 2x + y is:

• A. 8
• B. 7
• C. 9
• D. 6

Answer 1

The Correct Option is B

To solve for \(2x + y\), we equate the corresponding elements of the given matrices:

\(\begin{bmatrix} 4x & 5x-7 \\ 4x & 2x+y\end{bmatrix}=\begin{bmatrix} x+6 & y \\ 7y-13 & 7\end{bmatrix}\)

1. For the first element:
   \(4x = x + 6\)
   Solve for \(x\):
   \[\begin{align*} 4x & = x + 6 \\ 4x - x & = 6 \\ 3x & = 6 \\ x & = 2 \end{align*}\]
2. For the second element:
   \(5x - 7 = y\)
   Substitute \(x = 2\):
   \[\begin{align*} 5(2) - 7 & = y \\ 10 - 7 & = y \\ y & = 3 \end{align*}\]
3. Confirming from the third element:
   \(4x = 7y - 13\)
   Substitute \(x = 2\) and check with \(y = 3\):
   \[\begin{align*} 4(2) & = 7(3) - 13 \\ 8 & = 21 - 13 \\ 8 & = 8 \quad \text{True} \end{align*}\]
4. Finally, for the fourth element:
   \(2x + y = 7\)
5. Calculate \(2x + y\) with \(x = 2\) and \(y = 3\):
   \[\begin{align*} 2(2) + 3 & = 7 \\ 4 + 3 & = 7 \end{align*}\]

Thus, the value of \(2x + y\) is 7.