Solve 3(1-3x)+4(x-2y)+2(y-2x)=15

$$3 ( 1 - 3 x ) + 4 ( x - 2 y ) + 2 ( y - 2 x ) = 15$$

Solve for x

$$x=\frac{-2y-4}{3}$$

Steps for Solving Linear Equation

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

$$3-9x+4\left(x-2y\right)+2\left(y-2x\right)=15$$

Use the distributive property to multiply 4 by x-2y.

$$3-9x+4x-8y+2\left(y-2x\right)=15$$

Combine -9x and 4x to get -5x.

$$3-5x-8y+2\left(y-2x\right)=15$$

Use the distributive property to multiply 2 by y-2x.

$$3-5x-8y+2y-4x=15$$

Combine -8y and 2y to get -6y.

$$3-5x-6y-4x=15$$

Combine -5x and -4x to get -9x.

$$3-9x-6y=15$$

Subtract 3 from both sides.

$$-9x-6y=15-3$$

Subtract 3 from 15 to get 12.

$$-9x-6y=12$$

Add 6y to both sides.

$$-9x=12+6y$$

The equation is in standard form.

$$-9x=6y+12$$

Divide both sides by -9.

$$\frac{-9x}{-9}=\frac{6y+12}{-9}$$

Dividing by -9 undoes the multiplication by -9.

$$x=\frac{6y+12}{-9}$$

Divide 12+6y by -9.

$$x=\frac{-2y-4}{3}$$

Solve for y

$$y=-\frac{3x}{2}-2$$

Steps for Solving Linear Equation

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

$$3-9x+4\left(x-2y\right)+2\left(y-2x\right)=15$$

Use the distributive property to multiply 4 by x-2y.

$$3-9x+4x-8y+2\left(y-2x\right)=15$$

Combine -9x and 4x to get -5x.

$$3-5x-8y+2\left(y-2x\right)=15$$

Use the distributive property to multiply 2 by y-2x.

$$3-5x-8y+2y-4x=15$$

Combine -8y and 2y to get -6y.

$$3-5x-6y-4x=15$$

Combine -5x and -4x to get -9x.

$$3-9x-6y=15$$

Subtract 3 from both sides.

$$-9x-6y=15-3$$

Subtract 3 from 15 to get 12.

$$-9x-6y=12$$

Add 9x to both sides.

$$-6y=12+9x$$

The equation is in standard form.

$$-6y=9x+12$$

Divide both sides by -6.

$$\frac{-6y}{-6}=\frac{9x+12}{-6}$$

Dividing by -6 undoes the multiplication by -6.

$$y=\frac{9x+12}{-6}$$

Divide 12+9x by -6.

$$y=-\frac{3x}{2}-2$$