Solve 7(x-1)-6y=5(x+y)

$$7(x-1)-6y=5(x+y)$$

Solve for x

$$x=\frac{11y+7}{2}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 7 by x-1.

$$7x-7-6y=5\left(x+y\right)$$

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

$$7x-7-6y=5x+5y$$

Subtract 5x from both sides.

$$7x-7-6y-5x=5y$$

Combine 7x and -5x to get 2x.

$$2x-7-6y=5y$$

Add 7 to both sides.

$$2x-6y=5y+7$$

Add 6y to both sides.

$$2x=5y+7+6y$$

Combine 5y and 6y to get 11y.

$$2x=11y+7$$

Divide both sides by 2.

$$\frac{2x}{2}=\frac{11y+7}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x=\frac{11y+7}{2}$$

Solve for y

$$y=\frac{2x-7}{11}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 7 by x-1.

$$7x-7-6y=5\left(x+y\right)$$

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

$$7x-7-6y=5x+5y$$

Subtract 5y from both sides.

$$7x-7-6y-5y=5x$$

Combine -6y and -5y to get -11y.

$$7x-7-11y=5x$$

Subtract 7x from both sides.

$$-7-11y=5x-7x$$

Combine 5x and -7x to get -2x.

$$-7-11y=-2x$$

Add 7 to both sides.

$$-11y=-2x+7$$

The equation is in standard form.

$$-11y=7-2x$$

Divide both sides by -11.

$$\frac{-11y}{-11}=\frac{7-2x}{-11}$$

Dividing by -11 undoes the multiplication by -11.

$$y=\frac{7-2x}{-11}$$

Divide -2x+7 by -11.

$$y=\frac{2x-7}{11}$$