Solve 13/7-1/5+27/18-21/28=frac{x}{y}

$$\frac { 13 } { 7 } - \frac { 1 } { 5 } + \frac { 27 } { 18 } - \frac { 21 } { 28 } = \frac { x } { y }$$

Solve for x

$$x=\frac{337y}{140}$$

$$y\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 1260y, the least common multiple of 7,5,18,28,y.

$$1260y\times \frac{13}{7}+1260y\left(-\frac{1}{5}\right)+70y\times 27-45y\times 21=1260x$$

Multiply 1260 and \frac{13}{7} to get 2340.

$$2340y+1260y\left(-\frac{1}{5}\right)+70y\times 27-45y\times 21=1260x$$

Multiply 1260 and -\frac{1}{5} to get -252.

$$2340y-252y+70y\times 27-45y\times 21=1260x$$

Combine 2340y and -252y to get 2088y.

$$2088y+70y\times 27-45y\times 21=1260x$$

Multiply 70 and 27 to get 1890.

$$2088y+1890y-45y\times 21=1260x$$

Combine 2088y and 1890y to get 3978y.

$$3978y-45y\times 21=1260x$$

Multiply 45 and 21 to get 945.

$$3978y-945y=1260x$$

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

$$1260x=3978y-945y$$

Combine 3978y and -945y to get 3033y.

$$1260x=3033y$$

Divide both sides by 1260.

$$\frac{1260x}{1260}=\frac{3033y}{1260}$$

Dividing by 1260 undoes the multiplication by 1260.

$$x=\frac{3033y}{1260}$$

Divide 3033y by 1260.

$$x=\frac{337y}{140}$$

Solve for y

$$y=\frac{140x}{337}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 1260y, the least common multiple of 7,5,18,28,y.

$$1260y\times \frac{13}{7}+1260y\left(-\frac{1}{5}\right)+70y\times 27-45y\times 21=1260x$$

Multiply 1260 and \frac{13}{7} to get 2340.

$$2340y+1260y\left(-\frac{1}{5}\right)+70y\times 27-45y\times 21=1260x$$

Multiply 1260 and -\frac{1}{5} to get -252.

$$2340y-252y+70y\times 27-45y\times 21=1260x$$

Combine 2340y and -252y to get 2088y.

$$2088y+70y\times 27-45y\times 21=1260x$$

Multiply 70 and 27 to get 1890.

$$2088y+1890y-45y\times 21=1260x$$

Combine 2088y and 1890y to get 3978y.

$$3978y-45y\times 21=1260x$$

Multiply 45 and 21 to get 945.

$$3978y-945y=1260x$$

Combine 3978y and -945y to get 3033y.

$$3033y=1260x$$

Divide both sides by 3033.

$$\frac{3033y}{3033}=\frac{1260x}{3033}$$

Dividing by 3033 undoes the multiplication by 3033.

$$y=\frac{1260x}{3033}$$

Divide 1260x by 3033.

$$y=\frac{140x}{337}$$

Variable y cannot be equal to 0.

$$y=\frac{140x}{337}\text{, }y\neq 0$$