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

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

Solve for x

$$x=\frac{5\left(y-3\right)}{2}$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{2}{5} by x-5.

$$y-5=\frac{2}{5}x-2$$

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

$$\frac{2}{5}x-2=y-5$$

Add 2 to both sides.

$$\frac{2}{5}x=y-5+2$$

Add -5 and 2 to get -3.

$$\frac{2}{5}x=y-3$$

Divide both sides of the equation by \frac{2}{5}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{2}{5}x}{\frac{2}{5}}=\frac{y-3}{\frac{2}{5}}$$

Dividing by \frac{2}{5} undoes the multiplication by \frac{2}{5}.

$$x=\frac{y-3}{\frac{2}{5}}$$

Divide y-3 by \frac{2}{5} by multiplying y-3 by the reciprocal of \frac{2}{5}.

$$x=\frac{5y-15}{2}$$

Solve for y

$$y=\frac{2x}{5}+3$$

Solution Steps

Use the distributive property to multiply \frac{2}{5} by x-5.

$$y-5=\frac{2}{5}x-2$$

Add 5 to both sides.

$$y=\frac{2}{5}x-2+5$$

Add -2 and 5 to get 3.

$$y=\frac{2}{5}x+3$$