1. **State the problem:** Solve the simultaneous equations using substitution method: $$3x + 1.4y = 0.1 \quad (1)$$ $$x - 3.6y = 10.2 \quad (2)$$ 2. **Isolate one variable:** From equation (2), isolate $x$: $$x = 3.6y + 10.2$$ 3. **Substitute into equation (1):** Replace $x$ in equation (1) with $3.6y + 10.2$: $$3(3.6y + 10.2) + 1.4y = 0.1$$ 4. **Expand and simplify:** $$10.8y + 30.6 + 1.4y = 0.1$$ Combine like terms: $$12.2y + 30.6 = 0.1$$ 5. **Isolate $y$:** $$12.2y = 0.1 - 30.6$$ $$12.2y = -30.5$$ 6. **Solve for $y$:** $$y = \frac{-30.5}{12.2}$$ Show cancellation: $$y = \frac{\cancel{-30.5}}{\cancel{12.2}} = -2.5$$ 7. **Substitute $y$ back to find $x$:** $$x = 3.6(-2.5) + 10.2$$ $$x = -9 + 10.2 = 1.2$$ **Final answer:** $$x = 1.2, \quad y = -2.5$$