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

$$( 4 y + 6 z - 1 ) + 3 y - 4 ( 5 x - 3 y - 1 ) = 9$$

Solve for x

$$x=\frac{3z}{10}+\frac{19y}{20}-\frac{3}{10}$$

Steps for Solving Linear Equation

Combine 4y and 3y to get 7y.

$$7y+6z-1-4\left(5x-3y-1\right)=9$$

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

$$7y+6z-1-20x+12y+4=9$$

Combine 7y and 12y to get 19y.

$$19y+6z-1-20x+4=9$$

Add -1 and 4 to get 3.

$$19y+6z+3-20x=9$$

Subtract 19y from both sides.

$$6z+3-20x=9-19y$$

Subtract 6z from both sides.

$$3-20x=9-19y-6z$$

Subtract 3 from both sides.

$$-20x=9-19y-6z-3$$

Subtract 3 from 9 to get 6.

$$-20x=6-19y-6z$$

The equation is in standard form.

$$-20x=6-6z-19y$$

Divide both sides by -20.

$$\frac{-20x}{-20}=\frac{6-6z-19y}{-20}$$

Dividing by -20 undoes the multiplication by -20.

$$x=\frac{6-6z-19y}{-20}$$

Divide 6-19y-6z by -20.

$$x=\frac{3z}{10}+\frac{19y}{20}-\frac{3}{10}$$

Solve for y

$$y=\frac{20x-6z+6}{19}$$

Steps for Solving Linear Equation

Combine 4y and 3y to get 7y.

$$7y+6z-1-4\left(5x-3y-1\right)=9$$

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

$$7y+6z-1-20x+12y+4=9$$

Combine 7y and 12y to get 19y.

$$19y+6z-1-20x+4=9$$

Add -1 and 4 to get 3.

$$19y+6z+3-20x=9$$

Subtract 6z from both sides.

$$19y+3-20x=9-6z$$

Subtract 3 from both sides.

$$19y-20x=9-6z-3$$

Subtract 3 from 9 to get 6.

$$19y-20x=6-6z$$

Add 20x to both sides.

$$19y=6-6z+20x$$

The equation is in standard form.

$$19y=20x-6z+6$$

Divide both sides by 19.

$$\frac{19y}{19}=\frac{20x-6z+6}{19}$$

Dividing by 19 undoes the multiplication by 19.

$$y=\frac{20x-6z+6}{19}$$