Malik solved this system of equations. \( \begin{array}{r}2 x+4 y=24 \\ 5 x+y=15\end{array} \) As the first step, he decided to solve for \( x \) in the first equation because it has a small, even number for the coefficient. Jill told him there was a more efficient way. What reason can Jill give for her statement? The variable \( y \) in the second equation has a coefficient of one so there will be fewer steps to the sofution. The variable \( x \) in the second equation has a coefficient of 5 so it will be easy to divide 15 by 5 . The variable \( y \) in the first equation is divisible by 2 so it will be the most efficient way to start. The variable \( y \) in the first equation has a larger even number. When dividing by 4 , the solution will be a smaller number.
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Jill could argue that solving for \( y \) in the second equation, where the coefficient is 1, is more efficient because it leads to a straightforward calculation. By isolating \( y \), the equation becomes \( y = 15 - 5x \), which is quick and direct, letting them focus on one variable at a time without needing to deal with larger coefficients or additional steps. In addition, if Malik were to solve for \( x \) in the first equation, he would have to manipulate the equation involving \( y \) later, possibly leading to more complex fractions. Instead, with the second equation's simpler form, Jill simplifies the entire process, avoiding unnecessary complications right from the start.
