a) \( \left\{\begin{array}{c}2 x+5 y=16 \\ x+3 y=6\end{array}\right. \)

To solve the system of equations given, we can use substitution or elimination. Let's use the elimination method. First, we'll align the two equations: 1) \( 2x + 5y = 16 \) 2) \( x + 3y = 6 \) To eliminate \(x\), we can multiply the second equation by 2, resulting in: \( 2x + 6y = 12 \) Now we have: 1) \( 2x + 5y = 16 \) 2) \( 2x + 6y = 12 \) Next, we subtract the first equation from the second: \((2x + 6y) - (2x + 5y) = 12 - 16\) This simplifies to: \(y = -4\) Now, substitute \(y = -4\) back into one of the original equations to find \(x\). Using the second equation: \(x + 3(-4) = 6\) This simplifies to: \(x - 12 = 6\) So, \(x = 18\). The solution to the system is \(x = 18\) and \(y = -4\).