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# If $\begin{bmatrix}2x + y & 4x\\5x - 7 & 4x\end{bmatrix}=\begin{bmatrix}7 & 7y - 13\\y & x + 6\end{bmatrix},$then the value of x,y is

$\begin{array}{1 1}(A)\quad x=3,y=1 & (B)\quad x=2,y=3\\(C)\quad x=2,y=4 & (D)\quad x=3,y=3\end{array}$

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A)
Toolbox:
• If the order of 2 matrices are equal, their corresponding elements are equal, i.e, if $A_{ij}=B_{ij}$, then any element $a_{ij}$ in matrix A is equal to corresponding element $b_{ij}$ in matrix B.
• We can then match the corresponding elements and solve the resulting equations to find the values of the unknown variables.
Step1:
Given:
$\begin{bmatrix}2x + y & 4x\\5x - 7 & 4x\end{bmatrix}=\begin{bmatrix}7 & 7y - 13\\y & x + 6\end{bmatrix}$
The given matrices are equal hence their corresponding elements should be equal
$\Rightarrow2x+y=7$--------(1)
4x=7y-13------(2)
5x-7=y------(3)
4x=x+6-----(4)
Step2:
From equ(4) we have
4x=x+6
4x-x=6
3x=6
x=2
Step3:
Replace the value of x in equation (1)
2x+y=7
2(2)+y=7
4+y=7
y=3.