\begin{align}2x+y & =13 \quad \quad \enclose{circle}{\color{black}{1}}\\
3x-2y & = 2 \; \quad \quad \enclose{circle}{\color{black}{2}} \end{align}
\begin{align} To \; equate \; coefficients\; of \; y\\
multiply \: eqn \; \enclose{circle}{\color{black}{1}} \; by \; 2\\
2(2x+y) & = 2(13)\\
4x+2y & = 26 \quad \;\enclose{circle}{\color{black}{3}}\\
Add \; eqn\; \enclose{circle}{\color{black}{2}} \; to \; eqn \; \enclose{circle}{\color{black}{3}}\\ to \; eliminate \; y \\
(4x+2y)+(3x-2y) & = 26+2\\
7x & = 28\\
x & = 4\\
By \;substitution \; into\; eqn\; \enclose{circle}{\color{black}{1}}\\
2(4)+y & = 13\\
y & =5 \end{align}
\begin{align}8y-2x & =28 \quad \quad \enclose{circle}{\color{black}{1}}\\
6x+7y & = 9 \quad \quad \enclose{circle}{\color{black}{2}} \end{align}
\begin{align} To \; equate \; coefficients\; of \; x\\
multiply \: eqn \; \enclose{circle}{\color{black}{1}} \; by \; 3\\
3(8y-2x) & = 3(28)\\
24y-6x & = 84 \quad \enclose{circle}{\color{black}{3}}\\
Add \; eqn\; \enclose{circle}{\color{black}{2}} \; to \; eqn \; \enclose{circle}{\color{black}{3}}\\ to \; eliminate \; x \\
(6x+7y)+(24y-6x) & = 9+84\\
31y & =93\\
y & =3\\
By \;substitution \; into\; eqn\; \enclose{circle}{\color{black}{1}}\\
8(3)-2x & = 28\\
-2x & =4\\
x & =-2 \end{align}
\begin{align}5x-2y & =11 \quad \quad \enclose{circle}{\color{black}{1}}\\
3y+15x & = 6 \quad \quad \enclose{circle}{\color{black}{2}} \end{align}
\begin{align} To \; equate \; coefficients\; of \; x\\
multiply \: eqn \; \enclose{circle}{\color{black}{1}} \; by \; 3\\
3(5x-2y) & =33\\
15x-6y & =33 \quad \enclose{circle}{\color{black}{3}}\\
Subtract \; eqn\; \enclose{circle}{\color{black}{2}} \; from \; eqn \; \enclose{circle}{\color{black}{3}}\\ to \; eliminate \; x \\
(15x-6y)-(3y+15x) & = 33-6\\
-9y & = 27\\
y & = -3\\
By \;substitution \; into\; eqn\; \enclose{circle}{\color{black}{1}}\\
5x-2(-3) & = 11\\
5x & =5\\
x & =1 \end{align}
\begin{align}-12x+10y & =-28 \quad \quad \enclose{circle}{\color{black}{1}}\\
3y-2x & = -2 \quad \quad \enclose{circle}{\color{black}{2}} \end{align}
\begin{align} To \; equate \; coefficients\; of \; x\\
multiply \: eqn \; \enclose{circle}{\color{black}{2}} \; by \; 6\\
6(3y-2x) & = 6(-2)\\
18y-12x & =-12 \quad \enclose{circle}{\color{black}{3}}\\
Subtract \; eqn \; \enclose{circle}{\color{black}{3}}\; from \; eqn\; \enclose{circle}{\color{black}{1}}\\ to \;eliminate\; x \\
(-12x+10y)-(18y-12x) & = -28-(-12)\\
-8y & = -16\\
y & = 2\\
By \;substitution \; into\; eqn\; \enclose{circle}{\color{black}{1}}\\
-12x+10(2) & = -28\\
-12x= & =-48\\
x & =4
\end{align}