Solve y+5=-6-10/7+5(x-1

$$y+5 = \frac{ -6-10 }{ 7+5 } (x-1$$

Solve for x

$$x=\frac{-3y-11}{4}$$

Steps for Solving Linear Equation

Subtract 10 from -6 to get -16.

$$y+5=\frac{-16}{7+5}\left(x-1\right)$$

Add 7 and 5 to get 12.

$$y+5=\frac{-16}{12}\left(x-1\right)$$

Reduce the fraction \frac{-16}{12} to lowest terms by extracting and canceling out 4.

$$y+5=-\frac{4}{3}\left(x-1\right)$$

Use the distributive property to multiply -\frac{4}{3} by x-1.

$$y+5=-\frac{4}{3}x+\frac{4}{3}$$

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

$$-\frac{4}{3}x+\frac{4}{3}=y+5$$

Subtract \frac{4}{3} from both sides.

$$-\frac{4}{3}x=y+5-\frac{4}{3}$$

Subtract \frac{4}{3} from 5 to get \frac{11}{3}.

$$-\frac{4}{3}x=y+\frac{11}{3}$$

Divide both sides of the equation by -\frac{4}{3}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{-\frac{4}{3}x}{-\frac{4}{3}}=\frac{y+\frac{11}{3}}{-\frac{4}{3}}$$

Dividing by -\frac{4}{3} undoes the multiplication by -\frac{4}{3}.

$$x=\frac{y+\frac{11}{3}}{-\frac{4}{3}}$$

Divide y+\frac{11}{3} by -\frac{4}{3} by multiplying y+\frac{11}{3} by the reciprocal of -\frac{4}{3}.

$$x=\frac{-3y-11}{4}$$

Solve for y

$$y=\frac{-4x-11}{3}$$

Solution Steps

Subtract 10 from -6 to get -16.

$$y+5=\frac{-16}{7+5}\left(x-1\right)$$

Add 7 and 5 to get 12.

$$y+5=\frac{-16}{12}\left(x-1\right)$$

Reduce the fraction \frac{-16}{12} to lowest terms by extracting and canceling out 4.

$$y+5=-\frac{4}{3}\left(x-1\right)$$

Use the distributive property to multiply -\frac{4}{3} by x-1.

$$y+5=-\frac{4}{3}x+\frac{4}{3}$$

Subtract 5 from both sides.

$$y=-\frac{4}{3}x+\frac{4}{3}-5$$

Subtract 5 from \frac{4}{3} to get -\frac{11}{3}.

$$y=-\frac{4}{3}x-\frac{11}{3}$$