Solve y=1500x+1800*(-3x+27)+2000*(21-x+3x-27)

$$y=1500x+1800 \times (-3x+27)+2000 \times (21-x+3x-27)$$

Solve for x

$$x=\frac{y-36600}{100}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 1800 by -3x+27.

$$y=1500x-5400x+48600+2000\left(21-x+3x-27\right)$$

Combine 1500x and -5400x to get -3900x.

$$y=-3900x+48600+2000\left(21-x+3x-27\right)$$

Combine -x and 3x to get 2x.

$$y=-3900x+48600+2000\left(21+2x-27\right)$$

Subtract 27 from 21 to get -6.

$$y=-3900x+48600+2000\left(-6+2x\right)$$

Use the distributive property to multiply 2000 by -6+2x.

$$y=-3900x+48600-12000+4000x$$

Subtract 12000 from 48600 to get 36600.

$$y=-3900x+36600+4000x$$

Combine -3900x and 4000x to get 100x.

$$y=100x+36600$$

Swap sides so that all variable terms are on the left hand side.

$$100x+36600=y$$

Subtract 36600 from both sides.

$$100x=y-36600$$

Divide both sides by 100.

$$\frac{100x}{100}=\frac{y-36600}{100}$$

Dividing by 100 undoes the multiplication by 100.

$$x=\frac{y-36600}{100}$$

Divide y-36600 by 100.

$$x=\frac{y}{100}-366$$

Solve for y

$$y=100\left(x+366\right)$$

Solution Steps

Use the distributive property to multiply 1800 by -3x+27.

$$y=1500x-5400x+48600+2000\left(21-x+3x-27\right)$$

Combine 1500x and -5400x to get -3900x.

$$y=-3900x+48600+2000\left(21-x+3x-27\right)$$

Combine -x and 3x to get 2x.

$$y=-3900x+48600+2000\left(21+2x-27\right)$$

Subtract 27 from 21 to get -6.

$$y=-3900x+48600+2000\left(-6+2x\right)$$

Use the distributive property to multiply 2000 by -6+2x.

$$y=-3900x+48600-12000+4000x$$

Subtract 12000 from 48600 to get 36600.

$$y=-3900x+36600+4000x$$

Combine -3900x and 4000x to get 100x.

$$y=100x+36600$$