Solve 12x-42y+3z=5x-9y+32z

$$12x-42y+3z=5x-9y+32z$$

Solve for x

$$x=\frac{33y+29z}{7}$$

Steps for Solving Linear Equation

Subtract 5x from both sides.

$$12x-42y+3z-5x=-9y+32z$$

Combine 12x and -5x to get 7x.

$$7x-42y+3z=-9y+32z$$

Add 42y to both sides.

$$7x+3z=-9y+32z+42y$$

Combine -9y and 42y to get 33y.

$$7x+3z=33y+32z$$

Subtract 3z from both sides.

$$7x=33y+32z-3z$$

Combine 32z and -3z to get 29z.

$$7x=33y+29z$$

Divide both sides by 7.

$$\frac{7x}{7}=\frac{33y+29z}{7}$$

Dividing by 7 undoes the multiplication by 7.

$$x=\frac{33y+29z}{7}$$

Solve for y

$$y=\frac{7x-29z}{33}$$

Steps for Solving Linear Equation

Add 9y to both sides.

$$12x-42y+3z+9y=5x+32z$$

Combine -42y and 9y to get -33y.

$$12x-33y+3z=5x+32z$$

Subtract 12x from both sides.

$$-33y+3z=5x+32z-12x$$

Combine 5x and -12x to get -7x.

$$-33y+3z=-7x+32z$$

Subtract 3z from both sides.

$$-33y=-7x+32z-3z$$

Combine 32z and -3z to get 29z.

$$-33y=-7x+29z$$

The equation is in standard form.

$$-33y=29z-7x$$

Divide both sides by -33.

$$\frac{-33y}{-33}=\frac{29z-7x}{-33}$$

Dividing by -33 undoes the multiplication by -33.

$$y=\frac{29z-7x}{-33}$$

Divide -7x+29z by -33.

$$y=\frac{7x-29z}{33}$$