Solve 3(x-y)+5(x-4)=1

$$3 ( x - y ) + 5 ( x - 4 ) = 1$$

Solve for x

$$x=\frac{3\left(y+7\right)}{8}$$

Steps for Solving Linear Equation

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

$$3x-3y+5\left(x-4\right)=1$$

Use the distributive property to multiply 5 by x-4.

$$3x-3y+5x-20=1$$

Combine 3x and 5x to get 8x.

$$8x-3y-20=1$$

Add 3y to both sides.

$$8x-20=1+3y$$

Add 20 to both sides.

$$8x=1+3y+20$$

Add 1 and 20 to get 21.

$$8x=21+3y$$

The equation is in standard form.

$$8x=3y+21$$

Divide both sides by 8.

$$\frac{8x}{8}=\frac{3y+21}{8}$$

Dividing by 8 undoes the multiplication by 8.

$$x=\frac{3y+21}{8}$$

Solve for y

$$y=\frac{8x}{3}-7$$

Steps for Solving Linear Equation

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

$$3x-3y+5\left(x-4\right)=1$$

Use the distributive property to multiply 5 by x-4.

$$3x-3y+5x-20=1$$

Combine 3x and 5x to get 8x.

$$8x-3y-20=1$$

Subtract 8x from both sides.

$$-3y-20=1-8x$$

Add 20 to both sides.

$$-3y=1-8x+20$$

Add 1 and 20 to get 21.

$$-3y=21-8x$$

Divide both sides by -3.

$$\frac{-3y}{-3}=\frac{21-8x}{-3}$$

Dividing by -3 undoes the multiplication by -3.

$$y=\frac{21-8x}{-3}$$

Divide 21-8x by -3.

$$y=\frac{8x}{3}-7$$