Show all steps to solve for x and y . \( \left[\begin{array}{c}5 x-2 \\ 18\end{array}\right]=\left[\begin{array}{c}8 \\ 6-2 y\end{array}\right] \)

To solve for \(x\) and \(y\), we start by setting the components of the two vectors equal to each other. This gives us two equations: 1. \(5x - 2 = 8\) 2. \(18 = 6 - 2y\) Now, let's solve them one by one. ### Step 1: Solve for \(x\) From the first equation: \[ 5x - 2 = 8 \] Add 2 to both sides: \[ 5x = 10 \] Now, divide by 5: \[ x = 2 \] ### Step 2: Solve for \(y\) Now, we take the second equation: \[ 18 = 6 - 2y \] Subtract 6 from both sides: \[ 12 = -2y \] Now, divide by -2: \[ y = -6 \] ### Final Solution Thus, the solution is \(x = 2\) and \(y = -6\).