1. \( \left\{\begin{array}{l}x+4 y=8 \\ 2 x+8 y=6\end{array}\right. \)
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To solve this system of equations, we can use the method of substitution or elimination. However, looking closely, we can see that the second equation is simply a multiple of the first equation (the first equation multiplied by 2 gives \(2x + 8y = 16\), which is different from the second equation \(2x + 8y = 6\)). This indicates that the two lines represented by these equations are parallel and will never intersect, therefore, there is no solution. Remember, when you encounter a system of equations that appears inconsistent, it’s always good to double-check the relationships between the equations to confirm they represent parallel lines or have no intersection points.
