Which of the following values of $x$ and $y$ satisfy the following equations I and II? I. $3x + y = 19$ II. $x - y = 9$

### Concept & Strategy This is a fundamental **Simultaneous Linear Equations** problem. The most efficient strategy here is the **Elimination Method**. Because the coefficients of $y$ in the two equations are exact opposites ($+1$ and $-1$), adding the two equations together will instantly eliminate $y$, allowing us to solve for $x$ immediately. ### Step-by-Step Solution * **Step 1: Align the equations** Eq I: $3x + y = 19$ Eq II: $x - y = 9$ * **Step 2: Add the equations vertically** Add the left sides together and the right sides together: $(3x + x) + (y - y) = 19 + 9$ $4x + 0 = 28$ $4x = 28$ * **Step 3: Solve for x** Divide both sides by 4: $$x = \frac{28}{4} = 7$$ * **Step 4: Solve for y** Substitute the value of $x$ back into the simpler equation (Eq II): $$7 - y = 9$$ $$-y = 9 - 7$$ $$-y = 2$$ $$y = -2$$ ### Exam Strategy & Shortcut For multiple-choice questions with simple linear equations, **Option Verification (Back-solving)** is often the fastest method. Just plug the options into Equation II ($x - y = 9$): (a) $-7 - (-2) = -5$ (Incorrect) (b) $-7 - 2 = -9$ (Incorrect) (c) $7 - (-2) = 9$ (Correct!) You found the answer in seconds without doing any formal algebra. Just quickly verify it with Eq I: $3(7) + (-2) = 21 - 2 = 19$. Done. ### Common Pitfall A common mistake is arithmetic errors with negative signs when substituting $x$ back in to find $y$. Many students reach $7 - y = 9$ and incorrectly calculate $y = 2$ instead of $y = -2$, which leads them straight to the trap Option (d). Always verify your final $x$ and $y$ in *both* original equations. ### Final Answer Therefore, the correct answer is **7, -2**.