1. **State the problem:** Solve the system of linear equations from set (4): $$\begin{cases} 4x + 3y = 17 \\ 7x + 4y = 26 \end{cases}$$ 2. **Formula and method:** We will use the method of elimination to solve for $x$ and $y$. The goal is to eliminate one variable by making the coefficients of that variable equal in both equations. 3. **Eliminate $y$:** Multiply the first equation by 4 and the second equation by 3 to align the coefficients of $y$: $$\begin{cases} 4(4x + 3y) = 4(17) \\ 3(7x + 4y) = 3(26) \end{cases}$$ which simplifies to: $$\begin{cases} 16x + 12y = 68 \\ 21x + 12y = 78 \end{cases}$$ 4. **Subtract the first new equation from the second:** $$ (21x + 12y) - (16x + 12y) = 78 - 68 $$ $$ 21x - \cancel{16x} + 12y - \cancel{12y} = 10 $$ $$ 5x = 10 $$ 5. **Solve for $x$:** $$ x = \frac{10}{5} = 2 $$ 6. **Substitute $x=2$ into the first original equation:** $$ 4(2) + 3y = 17 $$ $$ 8 + 3y = 17 $$ 7. **Solve for $y$:** $$ 3y = 17 - 8 $$ $$ 3y = 9 $$ $$ y = \frac{9}{3} = 3 $$ **Final answer:** $$ (x, y) = (2, 3) $$