Solve -5(9-y)/9=7(y-2)/-3

$$\frac { - 5 ( 9 - y ) } { 9 } = \frac { 7 ( y - 2 ) } { - 3 }$$

Solve for y

$$y = \frac{87}{26} = 3\frac{9}{26} \approx 3.346153846$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 9, the least common multiple of 9,-3.

$$-5\left(9-y\right)=-3\times 7\left(y-2\right)$$

Use the distributive property to multiply -5 by 9-y.

$$-45+5y=-3\times 7\left(y-2\right)$$

Multiply -3 and 7 to get -21.

$$-45+5y=-21\left(y-2\right)$$

Use the distributive property to multiply -21 by y-2.

$$-45+5y=-21y+42$$

Add 21y to both sides.

$$-45+5y+21y=42$$

Combine 5y and 21y to get 26y.

$$-45+26y=42$$

Add 45 to both sides.

$$26y=42+45$$

Add 42 and 45 to get 87.

$$26y=87$$

Divide both sides by 26.

$$y=\frac{87}{26}$$