\begin{tabular}{l} Question 3 \\ Select the solution to the following system of equations: \\ \( \begin{array}{l}4 x+2 y=4 \\ 3 x-y=-7\end{array} \) \\ \( \begin{array}{l}x=1 \\ y=-4 \\ y=-4\end{array} \) \\ \( \begin{array}{l}x=-4 \\ y=1\end{array} \) \\ \( \begin{array}{l}x=-1 \\ y=4\end{array} \) \\ \hline\end{tabular}

To solve the system of equations given by \(4x + 2y = 4\) and \(3x - y = -7\), let’s first simplify the first equation: 1. Divide the entire equation \(4x + 2y = 4\) by 2: \[ 2x + y = 2 \] Now, we can express \(y\) in terms of \(x\): \[ y = 2 - 2x \] 2. Substitute \(y = 2 - 2x\) into the second equation \(3x - y = -7\): \[ 3x - (2 - 2x) = -7 \] Simplifying gives: \[ 3x - 2 + 2x = -7 \] Combine like terms: \[ 5x - 2 = -7 \] Adding 2 on both sides: \[ 5x = -5 \] Dividing by 5: \[ x = -1 \] 3. Now substitute \(x = -1\) back into the expression for \(y\): \[ y = 2 - 2(-1) = 2 + 2 = 4 \] So, the solution to the system of equations is \(x = -1\) and \(y = 4\). The correct answer among the options is \(x = -1\) and \(y = 4\). For a fun twist, math like solving systems of equations isn’t just about crunching numbers, it helps you develop critical thinking skills! Just think of it like solving a mystery where every equation is a clue leading you to the truth. Understanding how to apply systems of equations helps in real-world scenarios like optimizing resources in business or even balancing chemical equations in science! The ability to find the intersection of two lines can inform you where two different factors meet at a point - just like decision-making in everyday life!