Solve 4(10x+y)=x+10y+9

$$4(10x+y)=x+10y+9$$

Solve for x

$$x=\frac{2y+3}{13}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4 by 10x+y.

$$40x+4y=x+10y+9$$

Subtract x from both sides.

$$40x+4y-x=10y+9$$

Combine 40x and -x to get 39x.

$$39x+4y=10y+9$$

Subtract 4y from both sides.

$$39x=10y+9-4y$$

Combine 10y and -4y to get 6y.

$$39x=6y+9$$

Divide both sides by 39.

$$\frac{39x}{39}=\frac{6y+9}{39}$$

Dividing by 39 undoes the multiplication by 39.

$$x=\frac{6y+9}{39}$$

Divide 6y+9 by 39.

$$x=\frac{2y+3}{13}$$

Solve for y

$$y=\frac{13x-3}{2}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4 by 10x+y.

$$40x+4y=x+10y+9$$

Subtract 10y from both sides.

$$40x+4y-10y=x+9$$

Combine 4y and -10y to get -6y.

$$40x-6y=x+9$$

Subtract 40x from both sides.

$$-6y=x+9-40x$$

Combine x and -40x to get -39x.

$$-6y=-39x+9$$

The equation is in standard form.

$$-6y=9-39x$$

Divide both sides by -6.

$$\frac{-6y}{-6}=\frac{9-39x}{-6}$$

Dividing by -6 undoes the multiplication by -6.

$$y=\frac{9-39x}{-6}$$

Divide -39x+9 by -6.

$$y=\frac{13x-3}{2}$$