Solve 0,1/y-6=0.6/y-5

$$\frac { 0,1 } { y - 6 } = \frac { 0.6 } { y - 5 }$$

Solve for y

$$y=6.2$$

Steps for Solving Linear Equation

Variable y cannot be equal to any of the values 5,6 since division by zero is not defined. Multiply both sides of the equation by \left(y-6\right)\left(y-5\right), the least common multiple of y-6,y-5.

$$\left(y-5\right)\times 0.1=\left(y-6\right)\times 0.6$$

Use the distributive property to multiply y-5 by 0.1.

$$0.1y-0.5=\left(y-6\right)\times 0.6$$

Use the distributive property to multiply y-6 by 0.6.

$$0.1y-0.5=0.6y-3.6$$

Subtract 0.6y from both sides.

$$0.1y-0.5-0.6y=-3.6$$

Combine 0.1y and -0.6y to get -0.5y.

$$-0.5y-0.5=-3.6$$

Add 0.5 to both sides.

$$-0.5y=-3.6+0.5$$

Add -3.6 and 0.5 to get -3.1.

$$-0.5y=-3.1$$

Divide both sides by -0.5.

$$y=\frac{-3.1}{-0.5}$$

Expand \frac{-3.1}{-0.5} by multiplying both numerator and the denominator by 10.

$$y=\frac{-31}{-5}$$

Fraction \frac{-31}{-5} can be simplified to \frac{31}{5} by removing the negative sign from both the numerator and the denominator.

$$y=\frac{31}{5}$$