Arithmetic Operation of Matrices

Algebra Level 1

Suppose that \(x\) and \(y\) satisfy the following equation:

\[\left(\begin{array}{cc}x& y \\2&1 \end{array}\right)\left(\begin{array}{cc}x&0 \\y& x \end{array}\right)=2\left(\begin{array}{cc}10&6-x \\3&0 \end{array}\right)+\left(\begin{array}{cc}5&2x \\4& x \end{array}\right).\]

Evaluate \(x+y.\)

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