We are given with matrix equation
\(\begin{bmatrix} 2x-y& 5 \\[0.3em] 3 &y\\[0.3em] \end{bmatrix}\)= \(\begin{bmatrix} 6& 5\\[0.3em] 3 & -2 \\[0.3em] \end{bmatrix}\)

We need to find the values of x and y. 

We know by the property of matrices,

  \(\begin{bmatrix} a_{11}& a_{12} \\[0.3em] a_{21} & a_{22} \\[0.3em] \end{bmatrix}\)= \(\begin{bmatrix} b_{11}& b_{12} \\[0.3em] b_{21} & b_{22} \\[0.3em] \end{bmatrix}\)

This implies,

a₁₁ = b₁₁, 

a₁₂ = b₁₂, 

a₂₁ = b₂₁ and 

a₂₂ = b₂₂

So, if we have

\(\begin{bmatrix} 2x-y& 5 \\[0.3em] 3 &y\\[0.3em] \end{bmatrix}\)= \(\begin{bmatrix} 6& 5\\[0.3em] 3 & -2 \\[0.3em] \end{bmatrix}\)

Corresponding elements of two matrices are equal. 

That is,

2x – y = 6 …(i) 

5 = 5 

3 = 3 

y = - 2 …(ii) 

To solve for x and y, 

We have equations (i) and (ii). 

From equation (ii), 

y = - 2 

Substituting y = - 2 in equation (i), we get 

2x – y = 6 

⇒ 2x – (- 2) = 6 

⇒ 2x + 2 = 6 

⇒ 2x = 6 – 2 

⇒ 2x = 4

⇒ x = \(\frac{4}{2}\) 

⇒ x = 2

Thus, 

We get x = 2 and y = - 2.