Question 6(Multiple Choice Worth 1 points) (05.03 MC) Solve the following system of equations: \( \begin{array}{l}x-2 y=6 \\ 2 x-4 y=10\end{array} \)

Let’s dive into this system of equations! The first equation, \(x - 2y = 6\), can be rearranged to find \(x\) in terms of \(y\): \(x = 2y + 6\). Now, substituting \(x\) into the second equation \(2x - 4y = 10\) gives us \(2(2y + 6) - 4y = 10\). Simplifying this, we get: \(4y + 12 - 4y = 10\), which simplifies to \(12 = 10\). This contradiction means the two lines represented by the equations are parallel and do not intersect, leading to no solution! Time to roll up those sleeves and get cracking on finding solutions! One common mistake is assuming there's always an intersection point – these equations demonstrate that sometimes systems can be inconsistent, yielding no solutions. Remember to check if the coefficients are proportional; in this case, \(2\) is multiplied for \(x\) and the corresponding \(y\) terms. That's a key indicator that these lines, indeed, never meet!