Solve 0.5x+x/y=0.86x+7

$$0.5 x + \frac { x } { y } = 0.86 x + 7$$

Solve for x

$$x=\frac{175y}{25-9y}$$

$$y\neq \frac{25}{9}\text{ and }y\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by y.

$$0.5xy+x=0.86xy+y\times 7$$

Subtract 0.86xy from both sides.

$$0.5xy+x-0.86xy=y\times 7$$

Combine 0.5xy and -0.86xy to get -0.36xy.

$$-0.36xy+x=y\times 7$$

Combine all terms containing x.

$$\left(-0.36y+1\right)x=y\times 7$$

The equation is in standard form.

$$\left(-\frac{9y}{25}+1\right)x=7y$$

Divide both sides by -0.36y+1.

$$\frac{\left(-\frac{9y}{25}+1\right)x}{-\frac{9y}{25}+1}=\frac{7y}{-\frac{9y}{25}+1}$$

Dividing by -0.36y+1 undoes the multiplication by -0.36y+1.

$$x=\frac{7y}{-\frac{9y}{25}+1}$$

Divide 7y by -0.36y+1.

$$x=-\frac{175y}{9y-25}$$

Solve for y

$$y=\frac{25x}{9x+175}$$

$$x\neq 0\text{ and }x\neq -\frac{175}{9}$$

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 y.

$$0.5xy+x=0.86xy+y\times 7$$

Subtract 0.86xy from both sides.

$$0.5xy+x-0.86xy=y\times 7$$

Combine 0.5xy and -0.86xy to get -0.36xy.

$$-0.36xy+x=y\times 7$$

Subtract y\times 7 from both sides.

$$-0.36xy+x-y\times 7=0$$

Multiply -1 and 7 to get -7.

$$-0.36xy+x-7y=0$$

Subtract x from both sides. Anything subtracted from zero gives its negation.

$$-0.36xy-7y=-x$$

Combine all terms containing y.

$$\left(-0.36x-7\right)y=-x$$

The equation is in standard form.

$$\left(-\frac{9x}{25}-7\right)y=-x$$

Divide both sides by -0.36x-7.

$$\frac{\left(-\frac{9x}{25}-7\right)y}{-\frac{9x}{25}-7}=-\frac{x}{-\frac{9x}{25}-7}$$

Dividing by -0.36x-7 undoes the multiplication by -0.36x-7.

$$y=-\frac{x}{-\frac{9x}{25}-7}$$

Divide -x by -0.36x-7.

$$y=\frac{25x}{9x+175}$$

Variable y cannot be equal to 0.

$$y=\frac{25x}{9x+175}\text{, }y\neq 0$$