Solve -1/5y+1/3=-1/4

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

Solve for y

$$y = \frac{35}{12} = 2\frac{11}{12} \approx 2.916666667$$

Steps for Solving Linear Equation

Subtract \frac{1}{3} from both sides.

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

Least common multiple of 4 and 3 is 12. Convert -\frac{1}{4} and \frac{1}{3} to fractions with denominator 12.

$$-\frac{1}{5}y=-\frac{3}{12}-\frac{4}{12}$$

Since -\frac{3}{12} and \frac{4}{12} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{5}y=\frac{-3-4}{12}$$

Subtract 4 from -3 to get -7.

$$-\frac{1}{5}y=-\frac{7}{12}$$

Multiply both sides by -5, the reciprocal of -\frac{1}{5}.

$$y=-\frac{7}{12}\left(-5\right)$$

Express -\frac{7}{12}\left(-5\right) as a single fraction.

$$y=\frac{-7\left(-5\right)}{12}$$

Multiply -7 and -5 to get 35.

$$y=\frac{35}{12}$$