Solve 2(4y+6z-1)+3y-4left(5x-3y-1right)=9

$$2(4y+6z-1)+3y-4 \left( 5x-3y-1 \right) = 9$$

Solve for x

$$x=\frac{3z}{5}+\frac{23y}{20}-\frac{7}{20}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by 4y+6z-1.

$$8y+12z-2+3y-4\left(5x-3y-1\right)=9$$

Combine 8y and 3y to get 11y.

$$11y+12z-2-4\left(5x-3y-1\right)=9$$

Use the distributive property to multiply -4 by 5x-3y-1.

$$11y+12z-2-20x+12y+4=9$$

Combine 11y and 12y to get 23y.

$$23y+12z-2-20x+4=9$$

Add -2 and 4 to get 2.

$$23y+12z+2-20x=9$$

Subtract 23y from both sides.

$$12z+2-20x=9-23y$$

Subtract 12z from both sides.

$$2-20x=9-23y-12z$$

Subtract 2 from both sides.

$$-20x=9-23y-12z-2$$

Subtract 2 from 9 to get 7.

$$-20x=7-23y-12z$$

The equation is in standard form.

$$-20x=7-12z-23y$$

Divide both sides by -20.

$$\frac{-20x}{-20}=\frac{7-12z-23y}{-20}$$

Dividing by -20 undoes the multiplication by -20.

$$x=\frac{7-12z-23y}{-20}$$

Divide 7-23y-12z by -20.

$$x=\frac{3z}{5}+\frac{23y}{20}-\frac{7}{20}$$

Solve for y

$$y=\frac{20x-12z+7}{23}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by 4y+6z-1.

$$8y+12z-2+3y-4\left(5x-3y-1\right)=9$$

Combine 8y and 3y to get 11y.

$$11y+12z-2-4\left(5x-3y-1\right)=9$$

Use the distributive property to multiply -4 by 5x-3y-1.

$$11y+12z-2-20x+12y+4=9$$

Combine 11y and 12y to get 23y.

$$23y+12z-2-20x+4=9$$

Add -2 and 4 to get 2.

$$23y+12z+2-20x=9$$

Subtract 12z from both sides.

$$23y+2-20x=9-12z$$

Subtract 2 from both sides.

$$23y-20x=9-12z-2$$

Subtract 2 from 9 to get 7.

$$23y-20x=7-12z$$

Add 20x to both sides.

$$23y=7-12z+20x$$

The equation is in standard form.

$$23y=20x-12z+7$$

Divide both sides by 23.

$$\frac{23y}{23}=\frac{20x-12z+7}{23}$$

Dividing by 23 undoes the multiplication by 23.

$$y=\frac{20x-12z+7}{23}$$