Consider the first equation. Factor $32=4^{2}\times 2$. Rewrite the square root of the product $\sqrt{4^{2}\times 2}$ as the product of square roots $\sqrt{4^{2}}\sqrt{2}$. Take the square root of $4^{2}$.
Factor $128=8^{2}\times 2$. Rewrite the square root of the product $\sqrt{8^{2}\times 2}$ as the product of square roots $\sqrt{8^{2}}\sqrt{2}$. Take the square root of $8^{2}$.
Combine $4\sqrt{2}$ and $8\sqrt{2}$ to get $12\sqrt{2}$.
$$12\sqrt{2}-\sqrt{18}+\sqrt{50}=k\sqrt{2}$$
Factor $18=3^{2}\times 2$. Rewrite the square root of the product $\sqrt{3^{2}\times 2}$ as the product of square roots $\sqrt{3^{2}}\sqrt{2}$. Take the square root of $3^{2}$.
$$12\sqrt{2}-3\sqrt{2}+\sqrt{50}=k\sqrt{2}$$
Combine $12\sqrt{2}$ and $-3\sqrt{2}$ to get $9\sqrt{2}$.
$$9\sqrt{2}+\sqrt{50}=k\sqrt{2}$$
Factor $50=5^{2}\times 2$. Rewrite the square root of the product $\sqrt{5^{2}\times 2}$ as the product of square roots $\sqrt{5^{2}}\sqrt{2}$. Take the square root of $5^{2}$.
$$9\sqrt{2}+5\sqrt{2}=k\sqrt{2}$$
Combine $9\sqrt{2}$ and $5\sqrt{2}$ to get $14\sqrt{2}$.
$$14\sqrt{2}=k\sqrt{2}$$
Swap sides so that all variable terms are on the left hand side.
$$k\sqrt{2}=14\sqrt{2}$$
Consider the second equation. Subtract $k$ from both sides.
$$l-k=0$$
To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.
$$\sqrt{2}k=14\sqrt{2},-k+l=0$$
Pick one of the two equations which is more simple to solve for $k$ by isolating $k$ on the left hand side of the equal sign.
$$\sqrt{2}k=14\sqrt{2}$$
Divide both sides by $\sqrt{2}$.
$$k=14$$
Substitute $14$ for $k$ in the other equation, $-k+l=0$.
