Solve y-9=6/7(x+7)

$$y-9= \frac{ 6 }{ 7 } (x+7)$$

Solve for x

$$x=\frac{7\left(y-15\right)}{6}$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{6}{7} by x+7.

$$y-9=\frac{6}{7}x+6$$

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

$$\frac{6}{7}x+6=y-9$$

Subtract 6 from both sides.

$$\frac{6}{7}x=y-9-6$$

Subtract 6 from -9 to get -15.

$$\frac{6}{7}x=y-15$$

Divide both sides of the equation by \frac{6}{7}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{6}{7}x}{\frac{6}{7}}=\frac{y-15}{\frac{6}{7}}$$

Dividing by \frac{6}{7} undoes the multiplication by \frac{6}{7}.

$$x=\frac{y-15}{\frac{6}{7}}$$

Divide y-15 by \frac{6}{7} by multiplying y-15 by the reciprocal of \frac{6}{7}.

$$x=\frac{7y}{6}-\frac{35}{2}$$

Solve for y

$$y=\frac{6x}{7}+15$$

Solution Steps

Use the distributive property to multiply \frac{6}{7} by x+7.

$$y-9=\frac{6}{7}x+6$$

Add 9 to both sides.

$$y=\frac{6}{7}x+6+9$$

Add 6 and 9 to get 15.

$$y=\frac{6}{7}x+15$$