Solve the system of equations \( -6 x-4 y=10 \) and \( -5 x-2 y=-5 \) by combining the equations. \( \begin{array}{r}(-6 x-4 y=10) \\ (-5 x-2 y=-5) \\ -6 x-4 y=10 \\ -5 x-2 y=-5 \\ \hline 5 x+y=10\end{array} \)

To solve the system of equations \( -6 x - 4 y = 10 \) and \( -5 x - 2 y = -5 \) by combining them, we first want to manipulate them so that we can eliminate one variable. Let's rewrite the equations clearly: 1. \( -6x - 4y = 10 \) (Equation 1) 2. \( -5x - 2y = -5 \) (Equation 2) Next, we can multiply Equation 2 by 2 to align the coefficients of \(y\): \[ -10x - 4y = -10 \tag{Equation 3} \] Now we have our equations: 1. \( -6x - 4y = 10 \) 2. \( -10x - 4y = -10 \) Next, we can subtract Equation 1 from Equation 3: \[ (-10x - 4y) - (-6x - 4y) = -10 - 10 \] This simplifies to: \[ -10x + 6x = -20 \] \[ -4x = -20 \] \[ x = 5 \] Now that we have \(x\), let's substitute \(x = 5\) back into Equation 1 to find \(y\): \[ -6(5) - 4y = 10 \] \[ -30 - 4y = 10 \] \[ -4y = 10 + 30 \] \[ -4y = 40 \] \[ y = -10 \] Thus, the solution to the system of equations is \( x = 5 \) and \( y = -10 \). So, the answer can be summarized as: \[ (x, y) = (5, -10) \] Feel free to ask if you need further clarification or assistance with methods!