Solve for \( x \) and \( v \) simultaneously if \( x+3 y-5=0 \) \( \begin{array}{l}2 x-6 y+2=0\end{array} \)

To solve for \( x \) and \( y \) simultaneously, we can use the equations provided. First, let's rewrite the equations: 1. \( x + 3y - 5 = 0 \) (let's call this Equation 1) 2. \( 2x - 6y + 2 = 0 \) (let's call this Equation 2) From Equation 1, we can express \( x \) in terms of \( y \): \[ x = 5 - 3y \] Next, we substitute this expression for \( x \) back into Equation 2: \[ 2(5 - 3y) - 6y + 2 = 0 \] Expanding this equation: \[ 10 - 6y - 6y + 2 = 0 \\ 12 - 12y = 0 \] Now, solving for \( y \): \[ 12y = 12 \\ y = 1 \] Next, we substitute \( y = 1 \) back into the expression for \( x \): \[ x = 5 - 3(1) = 5 - 3 = 2 \] Thus, the solution is: \[ x = 2 \quad \text{and} \quad y = 1 \]