1. **State the problem:** Solve the system of linear equations: $$6x - y = 25$$ $$4x + 3y = 57$$ 2. **Use substitution or elimination method:** Here, elimination is convenient. 3. Multiply the first equation by 3 to align coefficients of $y$: $$3(6x - y) = 3(25) \Rightarrow 18x - 3y = 75$$ 4. Write the second equation: $$4x + 3y = 57$$ 5. Add the two equations to eliminate $y$: $$18x - 3y + 4x + 3y = 75 + 57$$ $$ (18x + 4x) + (-3y + 3y) = 132$$ $$22x + \cancel{-3y + 3y} = 132$$ $$22x = 132$$ 6. Solve for $x$: $$x = \frac{132}{22} = 6$$ 7. Substitute $x=6$ into the first original equation to find $y$: $$6(6) - y = 25$$ $$36 - y = 25$$ 8. Solve for $y$: $$-y = 25 - 36$$ $$-y = -11$$ $$y = 11$$ **Final answer:** $$x = 6, \quad y = 11$$