1. **State the problem:** Solve the simultaneous linear equations for variables $x$ and $y$. 2. **General form:** A system of two linear equations can be written as: $$a_1x + b_1y = c_1$$ $$a_2x + b_2y = c_2$$ where $a_1, b_1, c_1, a_2, b_2, c_2$ are constants. 3. **Method:** We can use substitution or elimination. Here, we use elimination. 4. **Example:** Suppose the system is: $$2x + 3y = 8$$ $$4x - y = 2$$ 5. **Eliminate $y$:** Multiply the second equation by 3 to align coefficients of $y$: $$3 \times (4x - y) = 3 \times 2$$ $$12x - 3y = 6$$ 6. **Add equations:** $$2x + 3y = 8$$ $$12x - 3y = 6$$ Adding gives: $$2x + 3y + 12x - 3y = 8 + 6$$ $$14x = 14$$ 7. **Solve for $x$:** $$x = \frac{14}{14} = 1$$ 8. **Substitute $x=1$ into first equation:** $$2(1) + 3y = 8$$ $$2 + 3y = 8$$ 9. **Solve for $y$:** $$3y = 8 - 2 = 6$$ $$y = \frac{6}{3} = 2$$ 10. **Final answer:** $$x = 1, \quad y = 2$$ This means the solution to the simultaneous equations is $x=1$ and $y=2$.