# Find the value of x from the following : $\begin{bmatrix} 2x-y & 5 \\ 3 & y \end{bmatrix} = \begin{bmatrix} 6 & 5 \\ 3 & -2 \end{bmatrix}$

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:
$\begin{bmatrix} 2x-y & 5 \\ 3 & y \end{bmatrix} = \begin{bmatrix} 6 & 5 \\ 3 & -2 \end{bmatrix}$
The above given two matrices are equal hence their corresponding elements should be equal.
2x-y=6-----(1)
y=-2------(2)
From equation (2) we get,
y=-2.
Step2:
Substitute the value of y in equation (1)
2x-(-2)=6
2x+2=6
2x=6-2
2x=4
x=2.