Question Find the solution of the system of equations. \[ \begin{array}{r}-6 x+2 y=16 \\ -7 x+6 y=26\end{array} \] Answer Attempt 1 out of 2

To solve the system of equations, we can use the substitution or elimination method. Here, we will use the elimination method. First, we can multiply the first equation by 3 to align the coefficients of \( y \): 1. \( -6x + 2y = 16 \) becomes \( -18x + 6y = 48 \). 2. Our system now looks like: \[ -18x + 6y = 48 \] \[ -7x + 6y = 26 \] Next, subtract the second equation from the first: \[ (-18x + 6y) - (-7x + 6y) = 48 - 26 \] This simplifies to: \[ -11x = 22 \] Solving for \( x \) gives us: \[ x = -2 \] Now, substitute \( x = -2 \) back into one of the original equations to find \( y \). Using the first equation: \[ -6(-2) + 2y = 16 \] \[ 12 + 2y = 16 \] \[ 2y = 4 \] \[ y = 2 \] Thus, the solution to the system of equations is \( x = -2, y = 2 \). For added context, the elimination method is particularly useful in systems where you can easily manipulate the equations to eliminate one variable. It's a technique used frequently in linear algebra and helps in efficiently solving multiple equations simultaneously. Also, when solving systems, always check your solution by plugging the values back into the original equations! This will confirm whether your calculations are correct and ensure no errors slipped through unnoticed.