1. **State the problem:** Solve the system of linear equations: $$3x + 2y = 49$$ $$4x - 3y = 3$$ 2. **Method:** We will use the elimination method to find $x$ and $y$. 3. **Eliminate one variable:** Multiply the first equation by 3 and the second by 2 to align coefficients of $y$: $$3(3x + 2y) = 3(49) \Rightarrow 9x + 6y = 147$$ $$2(4x - 3y) = 2(3) \Rightarrow 8x - 6y = 6$$ 4. **Add the two equations to eliminate $y$:** $$9x + 6y + 8x - 6y = 147 + 6 \Rightarrow (9x + 8x) + (6y - 6y) = 153$$ $$17x + \cancel{6y - 6y} = 153$$ $$17x = 153$$ 5. **Solve for $x$:** $$x = \frac{153}{17}$$ $$x = 9$$ 6. **Substitute $x=9$ into the first equation to find $y$:** $$3(9) + 2y = 49$$ $$27 + 2y = 49$$ 7. **Solve for $y$:** $$2y = 49 - 27$$ $$2y = 22$$ $$y = \frac{22}{2}$$ $$y = 11$$ **Final answer:** $$x = 9, \quad y = 11$$