Solve 1911(x+y)+105(x-y)=2016*1900

$$1911(x+y)+105(x-y)=2016 \times 1900$$

Solve for x

$$x=-\frac{43y}{48}+1900$$

Steps for Solving Linear Equation

Use the distributive property to multiply 1911 by x+y.

$$1911x+1911y+105\left(x-y\right)=2016\times 1900$$

Use the distributive property to multiply 105 by x-y.

$$1911x+1911y+105x-105y=2016\times 1900$$

Combine 1911x and 105x to get 2016x.

$$2016x+1911y-105y=2016\times 1900$$

Combine 1911y and -105y to get 1806y.

$$2016x+1806y=2016\times 1900$$

Multiply 2016 and 1900 to get 3830400.

$$2016x+1806y=3830400$$

Subtract 1806y from both sides.

$$2016x=3830400-1806y$$

Divide both sides by 2016.

$$\frac{2016x}{2016}=\frac{3830400-1806y}{2016}$$

Dividing by 2016 undoes the multiplication by 2016.

$$x=\frac{3830400-1806y}{2016}$$

Divide 3830400-1806y by 2016.

$$x=-\frac{43y}{48}+1900$$

Solve for y

$$y=\frac{91200-48x}{43}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 1911 by x+y.

$$1911x+1911y+105\left(x-y\right)=2016\times 1900$$

Use the distributive property to multiply 105 by x-y.

$$1911x+1911y+105x-105y=2016\times 1900$$

Combine 1911x and 105x to get 2016x.

$$2016x+1911y-105y=2016\times 1900$$

Combine 1911y and -105y to get 1806y.

$$2016x+1806y=2016\times 1900$$

Multiply 2016 and 1900 to get 3830400.

$$2016x+1806y=3830400$$

Subtract 2016x from both sides.

$$1806y=3830400-2016x$$

Divide both sides by 1806.

$$\frac{1806y}{1806}=\frac{3830400-2016x}{1806}$$

Dividing by 1806 undoes the multiplication by 1806.

$$y=\frac{3830400-2016x}{1806}$$

Divide 3830400-2016x by 1806.

$$y=\frac{91200-48x}{43}$$