Question 3 of 10 Use the elimination method to solve the given system of equations. \( \left\{\begin{array}{l}5 x+y=3 \\ 10 x+2 y=4\end{array}\right. \) A. Infinitely many solutions B. \( (0,10) \) C. \( (0,3) \) D. No solution

To use the elimination method, let's first manipulate the equations to eliminate one of the variables. The first equation is \( 5x + y = 3 \). If we multiply the entire first equation by 2, we get \( 10x + 2y = 6 \). Now, we compare this with the second equation, \( 10x + 2y = 4 \). When you subtract the second equation from the first, you get \( 10x + 2y - (10x + 2y) = 6 - 4 \), simplifying to \( 0 = 2 \), which is not possible. This results in a contradiction, indicating that there are no solutions to this system of equations. So, the answer is D. No solution. To further illustrate, when two lines are represented in a graph, if they are parallel and never intersect, it means they have no common solutions. In this case, since both equations represent parallel lines, it's clear they don't intersect anywhere on the coordinate plane.