Solve y-7=2-5/7+2left(x+2right)

$$y-7 = \frac{ 2-5 }{ 7+2 } \left( x+2 \right)$$

Solve for x

$$x=19-3y$$

Steps for Solving Linear Equation

Subtract 5 from 2 to get -3.

$$y-7=\frac{-3}{7+2}\left(x+2\right)$$

Add 7 and 2 to get 9.

$$y-7=\frac{-3}{9}\left(x+2\right)$$

Reduce the fraction \frac{-3}{9} to lowest terms by extracting and canceling out 3.

$$y-7=-\frac{1}{3}\left(x+2\right)$$

Use the distributive property to multiply -\frac{1}{3} by x+2.

$$y-7=-\frac{1}{3}x-\frac{2}{3}$$

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

$$-\frac{1}{3}x-\frac{2}{3}=y-7$$

Add \frac{2}{3} to both sides.

$$-\frac{1}{3}x=y-7+\frac{2}{3}$$

Add -7 and \frac{2}{3} to get -\frac{19}{3}.

$$-\frac{1}{3}x=y-\frac{19}{3}$$

Multiply both sides by -3.

$$\frac{-\frac{1}{3}x}{-\frac{1}{3}}=\frac{y-\frac{19}{3}}{-\frac{1}{3}}$$

Dividing by -\frac{1}{3} undoes the multiplication by -\frac{1}{3}.

$$x=\frac{y-\frac{19}{3}}{-\frac{1}{3}}$$

Divide y-\frac{19}{3} by -\frac{1}{3} by multiplying y-\frac{19}{3} by the reciprocal of -\frac{1}{3}.

$$x=19-3y$$

Solve for y

$$y=\frac{19-x}{3}$$

Solution Steps

Subtract 5 from 2 to get -3.

$$y-7=\frac{-3}{7+2}\left(x+2\right)$$

Add 7 and 2 to get 9.

$$y-7=\frac{-3}{9}\left(x+2\right)$$

Reduce the fraction \frac{-3}{9} to lowest terms by extracting and canceling out 3.

$$y-7=-\frac{1}{3}\left(x+2\right)$$

Use the distributive property to multiply -\frac{1}{3} by x+2.

$$y-7=-\frac{1}{3}x-\frac{2}{3}$$

Add 7 to both sides.

$$y=-\frac{1}{3}x-\frac{2}{3}+7$$

Add -\frac{2}{3} and 7 to get \frac{19}{3}.

$$y=-\frac{1}{3}x+\frac{19}{3}$$