Solve y+6/19/x-frac{16{19}}=3/8+frac{6/19}{frac{1}{4}-frac{16}{19}}

$$\frac { y + \frac { 6 } { 19 } } { x - \frac { 16 } { 19 } } = \frac { \frac { 3 } { 8 } + \frac { 6 } { 19 } } { \frac { 1 } { 4 } - \frac { 16 } { 19 } }$$

Solve for x

$$x=\frac{4-6y}{7}$$

$$y\neq -\frac{6}{19}$$

Steps for Solving Linear Equation

Factor the expressions that are not already factored in \frac{y+\frac{6}{19}}{x-\frac{16}{19}}.

$$\frac{\frac{1}{19}\left(19y+6\right)}{\frac{1}{19}\left(19x-16\right)}=\frac{\frac{3}{8}+\frac{6}{19}}{\frac{1}{4}-\frac{16}{19}}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{19y+6}{\left(\frac{1}{19}\right)^{0}\left(19x-16\right)}=\frac{\frac{3}{8}+\frac{6}{19}}{\frac{1}{4}-\frac{16}{19}}$$

Calculate \frac{1}{19} to the power of 0 and get 1.

$$\frac{19y+6}{1\left(19x-16\right)}=\frac{\frac{3}{8}+\frac{6}{19}}{\frac{1}{4}-\frac{16}{19}}$$

Add \frac{3}{8} and \frac{6}{19} to get \frac{105}{152}.

$$\frac{19y+6}{1\left(19x-16\right)}=\frac{\frac{105}{152}}{\frac{1}{4}-\frac{16}{19}}$$

Subtract \frac{16}{19} from \frac{1}{4} to get -\frac{45}{76}.

$$\frac{19y+6}{1\left(19x-16\right)}=\frac{\frac{105}{152}}{-\frac{45}{76}}$$

Divide \frac{105}{152} by -\frac{45}{76} by multiplying \frac{105}{152} by the reciprocal of -\frac{45}{76}.

$$\frac{19y+6}{1\left(19x-16\right)}=\frac{105}{152}\left(-\frac{76}{45}\right)$$

Multiply \frac{105}{152} and -\frac{76}{45} to get -\frac{7}{6}.

$$\frac{19y+6}{1\left(19x-16\right)}=-\frac{7}{6}$$

Use the distributive property to multiply 1 by 19x-16.

$$\frac{19y+6}{19x-16}=-\frac{7}{6}$$

Variable x cannot be equal to \frac{16}{19} since division by zero is not defined. Multiply both sides of the equation by 6\left(19x-16\right), the least common multiple of 19x-16,6.

$$6\left(19y+6\right)=-7\left(19x-16\right)$$

Use the distributive property to multiply 6 by 19y+6.

$$114y+36=-7\left(19x-16\right)$$

Use the distributive property to multiply -7 by 19x-16.

$$114y+36=-133x+112$$

Swap sides so that all variable terms are on the left hand side.

$$-133x+112=114y+36$$

Subtract 112 from both sides.

$$-133x=114y+36-112$$

Subtract 112 from 36 to get -76.

$$-133x=114y-76$$

Divide both sides by -133.

$$\frac{-133x}{-133}=\frac{114y-76}{-133}$$

Dividing by -133 undoes the multiplication by -133.

$$x=\frac{114y-76}{-133}$$

Divide 114y-76 by -133.

$$x=\frac{4-6y}{7}$$

Variable x cannot be equal to \frac{16}{19}.

$$x=\frac{4-6y}{7}\text{, }x\neq \frac{16}{19}$$

Solve for y

$$y=-\frac{7x}{6}+\frac{2}{3}$$

$$x\neq \frac{16}{19}$$

Steps for Solving Linear Equation

Factor the expressions that are not already factored in \frac{y+\frac{6}{19}}{x-\frac{16}{19}}.

$$\frac{\frac{1}{19}\left(19y+6\right)}{\frac{1}{19}\left(19x-16\right)}=\frac{\frac{3}{8}+\frac{6}{19}}{\frac{1}{4}-\frac{16}{19}}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{19y+6}{\left(\frac{1}{19}\right)^{0}\left(19x-16\right)}=\frac{\frac{3}{8}+\frac{6}{19}}{\frac{1}{4}-\frac{16}{19}}$$

Calculate \frac{1}{19} to the power of 0 and get 1.

$$\frac{19y+6}{1\left(19x-16\right)}=\frac{\frac{3}{8}+\frac{6}{19}}{\frac{1}{4}-\frac{16}{19}}$$

Add \frac{3}{8} and \frac{6}{19} to get \frac{105}{152}.

$$\frac{19y+6}{1\left(19x-16\right)}=\frac{\frac{105}{152}}{\frac{1}{4}-\frac{16}{19}}$$

Subtract \frac{16}{19} from \frac{1}{4} to get -\frac{45}{76}.

$$\frac{19y+6}{1\left(19x-16\right)}=\frac{\frac{105}{152}}{-\frac{45}{76}}$$

Divide \frac{105}{152} by -\frac{45}{76} by multiplying \frac{105}{152} by the reciprocal of -\frac{45}{76}.

$$\frac{19y+6}{1\left(19x-16\right)}=\frac{105}{152}\left(-\frac{76}{45}\right)$$

Multiply \frac{105}{152} and -\frac{76}{45} to get -\frac{7}{6}.

$$\frac{19y+6}{1\left(19x-16\right)}=-\frac{7}{6}$$

Use the distributive property to multiply 1 by 19x-16.

$$\frac{19y+6}{19x-16}=-\frac{7}{6}$$

Multiply both sides of the equation by 6\left(19x-16\right), the least common multiple of 19x-16,6.

$$6\left(19y+6\right)=-7\left(19x-16\right)$$

Use the distributive property to multiply 6 by 19y+6.

$$114y+36=-7\left(19x-16\right)$$

Use the distributive property to multiply -7 by 19x-16.

$$114y+36=-133x+112$$

Subtract 36 from both sides.

$$114y=-133x+112-36$$

Subtract 36 from 112 to get 76.

$$114y=-133x+76$$

The equation is in standard form.

$$114y=76-133x$$

Divide both sides by 114.

$$\frac{114y}{114}=\frac{76-133x}{114}$$

Dividing by 114 undoes the multiplication by 114.

$$y=\frac{76-133x}{114}$$

Divide -133x+76 by 114.

$$y=-\frac{7x}{6}+\frac{2}{3}$$