Solve 21-63/4y+15/2y-5/2=19/4

$$21 - \frac { 63 } { 4 } y + \frac { 15 } { 2 } y - \frac { 5 } { 2 } = \frac { 19 } { 4 }$$

Solve for y

$$y = \frac{5}{3} = 1\frac{2}{3} \approx 1.666666667$$

Steps for Solving Linear Equation

Combine -\frac{63}{4}y and \frac{15}{2}y to get -\frac{33}{4}y.

$$21-\frac{33}{4}y-\frac{5}{2}=\frac{19}{4}$$

Convert 21 to fraction \frac{42}{2}.

$$\frac{42}{2}-\frac{33}{4}y-\frac{5}{2}=\frac{19}{4}$$

Since \frac{42}{2} and \frac{5}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{42-5}{2}-\frac{33}{4}y=\frac{19}{4}$$

Subtract 5 from 42 to get 37.

$$\frac{37}{2}-\frac{33}{4}y=\frac{19}{4}$$

Subtract \frac{37}{2} from both sides.

$$-\frac{33}{4}y=\frac{19}{4}-\frac{37}{2}$$

Least common multiple of 4 and 2 is 4. Convert \frac{19}{4} and \frac{37}{2} to fractions with denominator 4.

$$-\frac{33}{4}y=\frac{19}{4}-\frac{74}{4}$$

Since \frac{19}{4} and \frac{74}{4} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{33}{4}y=\frac{19-74}{4}$$

Subtract 74 from 19 to get -55.

$$-\frac{33}{4}y=-\frac{55}{4}$$

Multiply both sides by -\frac{4}{33}, the reciprocal of -\frac{33}{4}.

$$y=-\frac{55}{4}\left(-\frac{4}{33}\right)$$

Multiply -\frac{55}{4} times -\frac{4}{33} by multiplying numerator times numerator and denominator times denominator.

$$y=\frac{-55\left(-4\right)}{4\times 33}$$

Do the multiplications in the fraction \frac{-55\left(-4\right)}{4\times 33}.

$$y=\frac{220}{132}$$

Reduce the fraction \frac{220}{132} to lowest terms by extracting and canceling out 44.

$$y=\frac{5}{3}$$