Solve -1/2=4-y/1-x

$$- \frac { 1 } { 2 } = \frac { 4 - y } { 1 - x }$$

Solve for x

$$x=9-2y$$

$$y\neq 4$$

Steps for Solving Linear Equation

Variable x cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by 2\left(x-1\right), the least common multiple of 2,1-x.

$$-\left(x-1\right)=-2\left(4-y\right)$$

To find the opposite of x-1, find the opposite of each term.

$$-x+1=-2\left(4-y\right)$$

Use the distributive property to multiply -2 by 4-y.

$$-x+1=-8+2y$$

Subtract 1 from both sides.

$$-x=-8+2y-1$$

Subtract 1 from -8 to get -9.

$$-x=-9+2y$$

The equation is in standard form.

$$-x=2y-9$$

Divide both sides by -1.

$$\frac{-x}{-1}=\frac{2y-9}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$x=\frac{2y-9}{-1}$$

Divide -9+2y by -1.

$$x=9-2y$$

Variable x cannot be equal to 1.

$$x=9-2y\text{, }x\neq 1$$

Solve for y

$$y=\frac{9-x}{2}$$

$$x\neq 1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2\left(x-1\right), the least common multiple of 2,1-x.

$$-\left(x-1\right)=-2\left(4-y\right)$$

To find the opposite of x-1, find the opposite of each term.

$$-x+1=-2\left(4-y\right)$$

Use the distributive property to multiply -2 by 4-y.

$$-x+1=-8+2y$$

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

$$-8+2y=-x+1$$

Add 8 to both sides.

$$2y=-x+1+8$$

Add 1 and 8 to get 9.

$$2y=-x+9$$

The equation is in standard form.

$$2y=9-x$$

Divide both sides by 2.

$$\frac{2y}{2}=\frac{9-x}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$y=\frac{9-x}{2}$$