Solve 7z+2+2x/5-3z+6y/8=-2

$$\frac{ 7z+2+2x }{ 5 } - \frac{ 3z+6y }{ 8 } =-2$$

Solve for x

$$x=\frac{15y}{8}-\frac{41z}{16}-6$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 40, the least common multiple of 5,8.

$$8\left(7z+2+2x\right)-5\left(3z+6y\right)=-80$$

Use the distributive property to multiply 8 by 7z+2+2x.

$$56z+16+16x-5\left(3z+6y\right)=-80$$

Use the distributive property to multiply -5 by 3z+6y.

$$56z+16+16x-15z-30y=-80$$

Combine 56z and -15z to get 41z.

$$41z+16+16x-30y=-80$$

Subtract 41z from both sides.

$$16+16x-30y=-80-41z$$

Subtract 16 from both sides.

$$16x-30y=-80-41z-16$$

Subtract 16 from -80 to get -96.

$$16x-30y=-96-41z$$

Add 30y to both sides.

$$16x=-96-41z+30y$$

The equation is in standard form.

$$16x=30y-41z-96$$

Divide both sides by 16.

$$\frac{16x}{16}=\frac{30y-41z-96}{16}$$

Dividing by 16 undoes the multiplication by 16.

$$x=\frac{30y-41z-96}{16}$$

Divide -96-41z+30y by 16.

$$x=\frac{15y}{8}-\frac{41z}{16}-6$$

Solve for y

$$y=\frac{8x}{15}+\frac{41z}{30}+\frac{16}{5}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 40, the least common multiple of 5,8.

$$8\left(7z+2+2x\right)-5\left(3z+6y\right)=-80$$

Use the distributive property to multiply 8 by 7z+2+2x.

$$56z+16+16x-5\left(3z+6y\right)=-80$$

Use the distributive property to multiply -5 by 3z+6y.

$$56z+16+16x-15z-30y=-80$$

Combine 56z and -15z to get 41z.

$$41z+16+16x-30y=-80$$

Subtract 41z from both sides.

$$16+16x-30y=-80-41z$$

Subtract 16 from both sides.

$$16x-30y=-80-41z-16$$

Subtract 16 from -80 to get -96.

$$16x-30y=-96-41z$$

Subtract 16x from both sides.

$$-30y=-96-41z-16x$$

The equation is in standard form.

$$-30y=-16x-41z-96$$

Divide both sides by -30.

$$\frac{-30y}{-30}=\frac{-16x-41z-96}{-30}$$

Dividing by -30 undoes the multiplication by -30.

$$y=\frac{-16x-41z-96}{-30}$$

Divide -96-41z-16x by -30.

$$y=\frac{8x}{15}+\frac{41z}{30}+\frac{16}{5}$$