Solve using the principles together. Check your answer. \[ 7 y-4=35-6 y \] The solution is \( y=\square \). (Type an integer or a simplified fraction.)

To solve the equation \( 7y - 4 = 35 - 6y \), we first want to get all the terms involving \( y \) on one side and constant terms on the other. 1. Add \( 6y \) to both sides: \[ 7y + 6y - 4 = 35 \] \[ 13y - 4 = 35 \] 2. Next, add 4 to both sides: \[ 13y = 35 + 4 \] \[ 13y = 39 \] 3. Finally, divide both sides by 13: \[ y = \frac{39}{13} \] \[ y = 3 \] So the solution is \( y = 3 \). Now let's check our answer by substituting \( y = 3 \) back into the original equation: Left side: \[ 7(3) - 4 = 21 - 4 = 17 \] Right side: \[ 35 - 6(3) = 35 - 18 = 17 \] Since both sides equal 17, the solution \( y = 3 \) is correct!