Solve 9(x-12/13)+7(y+11/39)+10(z+116/39)=0

$$9 ( x - \frac { 12 } { 13 } ) + 7 ( y + \frac { 11 } { 39 } ) + 10 ( z + \frac { 116 } { 39 } ) = 0$$

Solve for x

$$x=-\frac{7y}{9}-\frac{10z}{9}-\frac{913}{351}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 9 by x-\frac{12}{13}.

$$9x-\frac{108}{13}+7\left(y+\frac{11}{39}\right)+10\left(z+\frac{116}{39}\right)=0$$

Use the distributive property to multiply 7 by y+\frac{11}{39}.

$$9x-\frac{108}{13}+7y+\frac{77}{39}+10\left(z+\frac{116}{39}\right)=0$$

Add -\frac{108}{13} and \frac{77}{39} to get -\frac{19}{3}.

$$9x-\frac{19}{3}+7y+10\left(z+\frac{116}{39}\right)=0$$

Use the distributive property to multiply 10 by z+\frac{116}{39}.

$$9x-\frac{19}{3}+7y+10z+\frac{1160}{39}=0$$

Add -\frac{19}{3} and \frac{1160}{39} to get \frac{913}{39}.

$$9x+\frac{913}{39}+7y+10z=0$$

Subtract \frac{913}{39} from both sides. Anything subtracted from zero gives its negation.

$$9x+7y+10z=-\frac{913}{39}$$

Subtract 7y from both sides.

$$9x+10z=-\frac{913}{39}-7y$$

Subtract 10z from both sides.

$$9x=-\frac{913}{39}-7y-10z$$

The equation is in standard form.

$$9x=-7y-10z-\frac{913}{39}$$

Divide both sides by 9.

$$\frac{9x}{9}=\frac{-7y-10z-\frac{913}{39}}{9}$$

Dividing by 9 undoes the multiplication by 9.

$$x=\frac{-7y-10z-\frac{913}{39}}{9}$$

Divide -\frac{913}{39}-7y-10z by 9.

$$x=-\frac{7y}{9}-\frac{10z}{9}-\frac{913}{351}$$

Solve for y

$$y=-\frac{9x}{7}-\frac{10z}{7}-\frac{913}{273}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 9 by x-\frac{12}{13}.

$$9x-\frac{108}{13}+7\left(y+\frac{11}{39}\right)+10\left(z+\frac{116}{39}\right)=0$$

Use the distributive property to multiply 7 by y+\frac{11}{39}.

$$9x-\frac{108}{13}+7y+\frac{77}{39}+10\left(z+\frac{116}{39}\right)=0$$

Add -\frac{108}{13} and \frac{77}{39} to get -\frac{19}{3}.

$$9x-\frac{19}{3}+7y+10\left(z+\frac{116}{39}\right)=0$$

Use the distributive property to multiply 10 by z+\frac{116}{39}.

$$9x-\frac{19}{3}+7y+10z+\frac{1160}{39}=0$$

Add -\frac{19}{3} and \frac{1160}{39} to get \frac{913}{39}.

$$9x+\frac{913}{39}+7y+10z=0$$

Subtract 9x from both sides. Anything subtracted from zero gives its negation.

$$\frac{913}{39}+7y+10z=-9x$$

Subtract \frac{913}{39} from both sides.

$$7y+10z=-9x-\frac{913}{39}$$

Subtract 10z from both sides.

$$7y=-9x-\frac{913}{39}-10z$$

The equation is in standard form.

$$7y=-9x-10z-\frac{913}{39}$$

Divide both sides by 7.

$$\frac{7y}{7}=\frac{-9x-10z-\frac{913}{39}}{7}$$

Dividing by 7 undoes the multiplication by 7.

$$y=\frac{-9x-10z-\frac{913}{39}}{7}$$

Divide -9x-\frac{913}{39}-10z by 7.

$$y=-\frac{9x}{7}-\frac{10z}{7}-\frac{913}{273}$$