Solve 18*(0.9*65x-35)+42*(y/10*100-50)=810

$$18 \cdot ( 0.9 \times 65 x - 35 ) + 42 \cdot ( \frac { y } { 10 } \cdot 100 - 50 ) = 810$$

Solve for x

$$x=\frac{1180-140y}{351}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 10.

$$180\left(0.9\times 65x-35\right)+420\left(\frac{y}{10}\times 100-50\right)=8100$$

Multiply 0.9 and 65 to get 58.5.

$$180\left(58.5x-35\right)+420\left(\frac{y}{10}\times 100-50\right)=8100$$

Use the distributive property to multiply 180 by 58.5x-35.

$$10530x-6300+420\left(\frac{y}{10}\times 100-50\right)=8100$$

Cancel out 10, the greatest common factor in 100 and 10.

$$10530x-6300+420\left(10y-50\right)=8100$$

Use the distributive property to multiply 420 by 10y-50.

$$10530x-6300+4200y-21000=8100$$

Subtract 21000 from -6300 to get -27300.

$$10530x-27300+4200y=8100$$

Add 27300 to both sides.

$$10530x+4200y=8100+27300$$

Add 8100 and 27300 to get 35400.

$$10530x+4200y=35400$$

Subtract 4200y from both sides.

$$10530x=35400-4200y$$

Divide both sides by 10530.

$$\frac{10530x}{10530}=\frac{35400-4200y}{10530}$$

Dividing by 10530 undoes the multiplication by 10530.

$$x=\frac{35400-4200y}{10530}$$

Divide 35400-4200y by 10530.

$$x=\frac{1180-140y}{351}$$

Solve for y

$$y=-\frac{351x}{140}+\frac{59}{7}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 10.

$$180\left(0.9\times 65x-35\right)+420\left(\frac{y}{10}\times 100-50\right)=8100$$

Multiply 0.9 and 65 to get 58.5.

$$180\left(58.5x-35\right)+420\left(\frac{y}{10}\times 100-50\right)=8100$$

Use the distributive property to multiply 180 by 58.5x-35.

$$10530x-6300+420\left(\frac{y}{10}\times 100-50\right)=8100$$

Cancel out 10, the greatest common factor in 100 and 10.

$$10530x-6300+420\left(10y-50\right)=8100$$

Use the distributive property to multiply 420 by 10y-50.

$$10530x-6300+4200y-21000=8100$$

Subtract 21000 from -6300 to get -27300.

$$10530x-27300+4200y=8100$$

Subtract 10530x from both sides.

$$-27300+4200y=8100-10530x$$

Add 27300 to both sides.

$$4200y=8100-10530x+27300$$

Add 8100 and 27300 to get 35400.

$$4200y=35400-10530x$$

Divide both sides by 4200.

$$\frac{4200y}{4200}=\frac{35400-10530x}{4200}$$

Dividing by 4200 undoes the multiplication by 4200.

$$y=\frac{35400-10530x}{4200}$$

Divide 35400-10530x by 4200.

$$y=-\frac{351x}{140}+\frac{59}{7}$$