Solve -7/5y+4/3=-1/3y-1

$$- \frac { 7 } { 5 } y + \frac { 4 } { 3 } = - \frac { 1 } { 3 } y - 1$$

Solve for y

$$y = \frac{35}{16} = 2\frac{3}{16} = 2.1875$$

Steps for Solving Linear Equation

Add \frac{1}{3}y to both sides.

$$-\frac{7}{5}y+\frac{4}{3}+\frac{1}{3}y=-1$$

Combine -\frac{7}{5}y and \frac{1}{3}y to get -\frac{16}{15}y.

$$-\frac{16}{15}y+\frac{4}{3}=-1$$

Subtract \frac{4}{3} from both sides.

$$-\frac{16}{15}y=-1-\frac{4}{3}$$

Convert -1 to fraction -\frac{3}{3}.

$$-\frac{16}{15}y=-\frac{3}{3}-\frac{4}{3}$$

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

$$-\frac{16}{15}y=\frac{-3-4}{3}$$

Subtract 4 from -3 to get -7.

$$-\frac{16}{15}y=-\frac{7}{3}$$

Multiply both sides by -\frac{15}{16}, the reciprocal of -\frac{16}{15}.

$$y=-\frac{7}{3}\left(-\frac{15}{16}\right)$$

Multiply -\frac{7}{3} times -\frac{15}{16} by multiplying numerator times numerator and denominator times denominator.

$$y=\frac{-7\left(-15\right)}{3\times 16}$$

Do the multiplications in the fraction \frac{-7\left(-15\right)}{3\times 16}.

$$y=\frac{105}{48}$$

Reduce the fraction \frac{105}{48} to lowest terms by extracting and canceling out 3.

$$y=\frac{35}{16}$$