\begin{align}4x+y & =10 \quad \quad \enclose{circle}{\color{black}{1}}\\
3x-y & = 11 \quad \quad \enclose{circle}{\color{black}{2}} \end{align}
\begin{align}
Add \; eqn \; \enclose{circle}{\color{black}{1}}\; to \; eqn\; \enclose{circle}{\color{black}{2}}\\ to \;eliminate\; y \\
(4x+y)+(3x-y) & = 10+11\\
7x & = 21\\
x & = 3\\
Then \; by \;substitution \\ into\; eqn\; \enclose{circle}{\color{black}{1}}\\
4(3)+y & = 10\\
y & =-2 \end{align}
\begin{align}4y+3x & =20 \quad \quad \enclose{circle}{\color{black}{1}}\\
-3x+2y & = -8 \quad \quad \enclose{circle}{\color{black}{2}} \end{align}
\begin{align} Add \; eqn \; \enclose{circle}{\color{black}{1}}\; to \; eqn\; \enclose{circle}{\color{black}{2}}\\ to \;eliminate\; x \\
(4y+3x)+(-3x+2y) & = 20-8\\
6y & = 12\\
y & = 2\\
Then \; by \;substitution \\ into\; eqn\; \enclose{circle}{\color{black}{1}}\\
4(2)+3x & = 20\\
3x & =12\\
x & =4 \end{align}
\begin{align}6x+4y & =18 \quad \quad \enclose{circle}{\color{black}{1}}\\
2x+4y & = 14 \quad \quad \enclose{circle}{\color{black}{2}} \end{align}
\begin{align} Subtract \; eqn \;\enclose{circle}{\color{black}{2}}\; from \; eqn\; \enclose{circle}{\color{black}{1}}\\ to \;eliminate\; y \\
(6x+4y)-(2x+4y) & = 18-14\\
4x & = 4\\
x & = 1\\
Then \; by \;substitution \\ into\; eqn\; \enclose{circle}{\color{black}{1}}\\
6(1)+4y & = 18\\
4y & =12\\
y & =3 \end{align}
\begin{align}-5x+2y & =2 \quad \quad \enclose{circle}{\color{black}{1}}\\
y-5x & = -4 \quad \quad \enclose{circle}{\color{black}{2}} \end{align}
\begin{align} Subtract \; eqn \; \enclose{circle}{\color{black}{2}}\; from \; eqn\; \enclose{circle}{\color{black}{1}}\\ to \;eliminate\; x \\
(-5x+2y)-(y-5x) & = 2-(-4)\\
y & = 6\\
Then \; by \;substitution \\ into\; eqn\; \enclose{circle}{\color{black}{1}}\\
-5x+2(6) & = 2\\
-5x= & =-10\\
x & =2
\end{align}