Solve y-5=6/7(x-2)

$$y - 5 = \frac { 6 } { 7 } ( x - 2 )$$

Solve for x

$$x=\frac{7y-23}{6}$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{6}{7} by x-2.

$$y-5=\frac{6}{7}x-\frac{12}{7}$$

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

$$\frac{6}{7}x-\frac{12}{7}=y-5$$

Add \frac{12}{7} to both sides.

$$\frac{6}{7}x=y-5+\frac{12}{7}$$

Add -5 and \frac{12}{7} to get -\frac{23}{7}.

$$\frac{6}{7}x=y-\frac{23}{7}$$

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

$$\frac{\frac{6}{7}x}{\frac{6}{7}}=\frac{y-\frac{23}{7}}{\frac{6}{7}}$$

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

$$x=\frac{y-\frac{23}{7}}{\frac{6}{7}}$$

Divide y-\frac{23}{7} by \frac{6}{7} by multiplying y-\frac{23}{7} by the reciprocal of \frac{6}{7}.

$$x=\frac{7y-23}{6}$$

Solve for y

$$y=\frac{6x+23}{7}$$

Solution Steps

Use the distributive property to multiply \frac{6}{7} by x-2.

$$y-5=\frac{6}{7}x-\frac{12}{7}$$

Add 5 to both sides.

$$y=\frac{6}{7}x-\frac{12}{7}+5$$

Add -\frac{12}{7} and 5 to get \frac{23}{7}.

$$y=\frac{6}{7}x+\frac{23}{7}$$