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# Find the value of x, if $\begin {bmatrix} 3x+y & -y \\ 2y-x & 3 \end{bmatrix} = \begin {bmatrix} 1 & 2 \\ -5 & 3 \end{bmatrix}$

$\begin{array}{1 1} x = 1\; y = -1 \\ x = 1\; y = -2 \\ x = 1\; y = 2 \\ x = 0\; y = -2 \end{array}$

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
$\begin {bmatrix} 3x+y & -y \\ 2y-x & 3 \end{bmatrix} = \begin {bmatrix} 1 & 2 \\ -5 & 3 \end{bmatrix}$
The given two matrices are equal,hence their corresponding elements should be equal.
$\Rightarrow -y=2$
y=-2.
Step2:
3x+y=1-----(1)
Substitute the value of y in equation (1),we get
3x-2=1
3x=3
x=1