Solve 5(x+2y)-(3x+13y)=14

$$5 ( x + 2 y ) - ( 3 x + 13 y ) = 14$$

Solve for x

$$x=\frac{3y}{2}+7$$

Steps for Solving Linear Equation

Use the distributive property to multiply 5 by x+2y.

$$5x+10y-\left(3x+13y\right)=14$$

To find the opposite of 3x+13y, find the opposite of each term.

$$5x+10y-3x-13y=14$$

Combine 5x and -3x to get 2x.

$$2x+10y-13y=14$$

Combine 10y and -13y to get -3y.

$$2x-3y=14$$

Add 3y to both sides.

$$2x=14+3y$$

The equation is in standard form.

$$2x=3y+14$$

Divide both sides by 2.

$$\frac{2x}{2}=\frac{3y+14}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x=\frac{3y+14}{2}$$

Divide 14+3y by 2.

$$x=\frac{3y}{2}+7$$

Solve for y

$$y=\frac{2\left(x-7\right)}{3}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 5 by x+2y.

$$5x+10y-\left(3x+13y\right)=14$$

To find the opposite of 3x+13y, find the opposite of each term.

$$5x+10y-3x-13y=14$$

Combine 5x and -3x to get 2x.

$$2x+10y-13y=14$$

Combine 10y and -13y to get -3y.

$$2x-3y=14$$

Subtract 2x from both sides.

$$-3y=14-2x$$

Divide both sides by -3.

$$\frac{-3y}{-3}=\frac{14-2x}{-3}$$

Dividing by -3 undoes the multiplication by -3.

$$y=\frac{14-2x}{-3}$$

Divide 14-2x by -3.

$$y=\frac{2x-14}{3}$$