Solve y-3=-2-3/-1-5(x-5)

$$y - 3 = \frac { - 2 - 3 } { - 1 - 5 } ( x - 5 )$$

Solve for x

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

Steps for Solving Linear Equation

Subtract 3 from -2 to get -5.

$$y-3=\frac{-5}{-1-5}\left(x-5\right)$$

Subtract 5 from -1 to get -6.

$$y-3=\frac{-5}{-6}\left(x-5\right)$$

Fraction \frac{-5}{-6} can be simplified to \frac{5}{6} by removing the negative sign from both the numerator and the denominator.

$$y-3=\frac{5}{6}\left(x-5\right)$$

Use the distributive property to multiply \frac{5}{6} by x-5.

$$y-3=\frac{5}{6}x-\frac{25}{6}$$

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

$$\frac{5}{6}x-\frac{25}{6}=y-3$$

Add \frac{25}{6} to both sides.

$$\frac{5}{6}x=y-3+\frac{25}{6}$$

Add -3 and \frac{25}{6} to get \frac{7}{6}.

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

Divide both sides of the equation by \frac{5}{6}, which is the same as multiplying both sides by the reciprocal of the fraction.

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

Dividing by \frac{5}{6} undoes the multiplication by \frac{5}{6}.

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

Divide y+\frac{7}{6} by \frac{5}{6} by multiplying y+\frac{7}{6} by the reciprocal of \frac{5}{6}.

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

Solve for y

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

Solution Steps

Subtract 3 from -2 to get -5.

$$y-3=\frac{-5}{-1-5}\left(x-5\right)$$

Subtract 5 from -1 to get -6.

$$y-3=\frac{-5}{-6}\left(x-5\right)$$

Fraction \frac{-5}{-6} can be simplified to \frac{5}{6} by removing the negative sign from both the numerator and the denominator.

$$y-3=\frac{5}{6}\left(x-5\right)$$

Use the distributive property to multiply \frac{5}{6} by x-5.

$$y-3=\frac{5}{6}x-\frac{25}{6}$$

Add 3 to both sides.

$$y=\frac{5}{6}x-\frac{25}{6}+3$$

Add -\frac{25}{6} and 3 to get -\frac{7}{6}.

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