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# If $\begin{bmatrix} x+3y & y \\ 7-x & 4 \end{bmatrix}=\begin{bmatrix} 4 & -1 \\ 0 & 4 \end{bmatrix}$, find the values of x and y.

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## 1 Answer

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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
$\begin{bmatrix} x+3y & y \\ 7-x & 4 \end{bmatrix}=\begin{bmatrix} 4 & -1 \\ 0 & 4 \end{bmatrix}$
The above given matrices are equal hence their corresponding elements should be equal.
x+3y=4------(1)
y=-1-------(2)
7-x=0-------(3)
Step2:
From equation(2) we have
y=-1
From equation (3) we have
7-x=0
-x=-7
x=7
Hence x=7,y=-1.
answered Apr 8, 2013

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