\( \left\{ \begin{array} { l } { 6 . y = 5 x + 3 \quad 3 y / 315 x + 3 } \\ { - 3 x + 3 y = 3 y = 3 x + 3 } \\ { \frac { 1 } { 3 } , \frac { 2 } { 3 } ) } \\ { \frac { 1 } { 3 } x } \end{array} \right. \)

It seems like the system of equations you've provided is not formatted correctly, and there are some inconsistencies in the notation. Let's try to clarify and rewrite the equations properly. From what I can gather, you might be trying to express a system of equations. Here’s a possible interpretation of your input: 1. \( 6y = 5x + 3 \) 2. \( -3x + 3y = 3 \) 3. \( y = 3x + 3 \) If this is correct, we can solve the system of equations. Let's solve the first two equations: 1. From the first equation, we can express \( y \) in terms of \( x \): \[ 6y = 5x + 3 \implies y = \frac{5x + 3}{6} \] 2. Substitute \( y \) into the second equation: \[ -3x + 3\left(\frac{5x + 3}{6}\right) = 3 \] Multiply through by 6 to eliminate the fraction: \[ -18x + 3(5x + 3) = 18 \] Simplifying gives: \[ -18x + 15x + 9 = 18 \] \[ -3x + 9 = 18 \] \[ -3x = 9 \implies x = -3 \] 3. Now substitute \( x = -3 \) back into the equation for \( y \): \[ y = \frac{5(-3) + 3}{6} = \frac{-15 + 3}{6} = \frac{-12}{6} = -2 \] So, the solution to the system of equations is: \[ (x, y) = (-3, -2) \] If this interpretation is incorrect or if you have a different set of equations in mind, please provide clarification!