Solve 6+13left(x-1right)=5+10(y-1)

$$6+13 \left( x-1 \right) = 5+10(y-1)$$

Solve for x

$$x=\frac{10y+2}{13}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 13 by x-1.

$$6+13x-13=5+10\left(y-1\right)$$

Subtract 13 from 6 to get -7.

$$-7+13x=5+10\left(y-1\right)$$

Use the distributive property to multiply 10 by y-1.

$$-7+13x=5+10y-10$$

Subtract 10 from 5 to get -5.

$$-7+13x=-5+10y$$

Add 7 to both sides.

$$13x=-5+10y+7$$

Add -5 and 7 to get 2.

$$13x=2+10y$$

The equation is in standard form.

$$13x=10y+2$$

Divide both sides by 13.

$$\frac{13x}{13}=\frac{10y+2}{13}$$

Dividing by 13 undoes the multiplication by 13.

$$x=\frac{10y+2}{13}$$

Solve for y

$$y=\frac{13x}{10}-\frac{1}{5}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 13 by x-1.

$$6+13x-13=5+10\left(y-1\right)$$

Subtract 13 from 6 to get -7.

$$-7+13x=5+10\left(y-1\right)$$

Use the distributive property to multiply 10 by y-1.

$$-7+13x=5+10y-10$$

Subtract 10 from 5 to get -5.

$$-7+13x=-5+10y$$

Swap sides so that all variable terms are on the left hand side.

$$-5+10y=-7+13x$$

Add 5 to both sides.

$$10y=-7+13x+5$$

Add -7 and 5 to get -2.

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

The equation is in standard form.

$$10y=13x-2$$

Divide both sides by 10.

$$\frac{10y}{10}=\frac{13x-2}{10}$$

Dividing by 10 undoes the multiplication by 10.

$$y=\frac{13x-2}{10}$$

Divide -2+13x by 10.

$$y=\frac{13x}{10}-\frac{1}{5}$$