Solve y-5/6y-6=1/9-y-3/4y-4

$$\frac { y - 5 } { 6 y - 6 } = \frac { 1 } { 9 } \frac { - y - 3 } { 4 y - 4 }$$

Solve for y

$$y = \frac{27}{7} = 3\frac{6}{7} \approx 3.857142857$$

Steps for Solving Linear Equation

Variable y cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by 36\left(y-1\right), the least common multiple of 6y-6,9,4y-4.

$$6\left(y-5\right)=\frac{1}{9}\times 9\left(-y-3\right)$$

Use the distributive property to multiply 6 by y-5.

$$6y-30=\frac{1}{9}\times 9\left(-y-3\right)$$

Multiply \frac{1}{9} and 9 to get 1.

$$6y-30=-y-3$$

Add y to both sides.

$$6y-30+y=-3$$

Combine 6y and y to get 7y.

$$7y-30=-3$$

Add 30 to both sides.

$$7y=-3+30$$

Add -3 and 30 to get 27.

$$7y=27$$

Divide both sides by 7.

$$y=\frac{27}{7}$$