Solve 1-x/1-y=3(4-x)/-1-y

$$\frac{ 1-x }{ 1-y } = \frac{ 3(4-x) }{ -1-y }$$

Solve for x (complex solution)

$$x=-\frac{11y-13}{2\left(2-y\right)}$$

$$y\neq 2\text{ and }y\neq 1\text{ and }y\neq -1$$

Steps for Solving Linear Equation

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

$$-\left(1+y\right)\left(1-x\right)=\left(1-y\right)\times 3\left(4-x\right)$$

To find the opposite of 1+y, find the opposite of each term.

$$\left(-1-y\right)\left(1-x\right)=\left(1-y\right)\times 3\left(4-x\right)$$

Use the distributive property to multiply -1-y by 1-x.

$$-1+x-y+yx=\left(1-y\right)\times 3\left(4-x\right)$$

Use the distributive property to multiply 1-y by 3.

$$-1+x-y+yx=\left(3-3y\right)\left(4-x\right)$$

Use the distributive property to multiply 3-3y by 4-x.

$$-1+x-y+yx=12-3x-12y+3yx$$

Add 3x to both sides.

$$-1+x-y+yx+3x=12-12y+3yx$$

Combine x and 3x to get 4x.

$$-1+4x-y+yx=12-12y+3yx$$

Subtract 3yx from both sides.

$$-1+4x-y+yx-3yx=12-12y$$

Combine yx and -3yx to get -2yx.

$$-1+4x-y-2yx=12-12y$$

Add 1 to both sides.

$$4x-y-2yx=12-12y+1$$

Add 12 and 1 to get 13.

$$4x-y-2yx=13-12y$$

Add y to both sides.

$$4x-2yx=13-12y+y$$

Combine -12y and y to get -11y.

$$4x-2yx=13-11y$$

Combine all terms containing x.

$$\left(4-2y\right)x=13-11y$$

Divide both sides by -2y+4.

$$\frac{\left(4-2y\right)x}{4-2y}=\frac{13-11y}{4-2y}$$

Dividing by -2y+4 undoes the multiplication by -2y+4.

$$x=\frac{13-11y}{4-2y}$$

Divide 13-11y by -2y+4.

$$x=\frac{13-11y}{2\left(2-y\right)}$$

Solve for x

$$x=-\frac{11y-13}{2\left(2-y\right)}$$

$$y\neq 2\text{ and }|y|\neq 1$$

Steps for Solving Linear Equation

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

$$-\left(1+y\right)\left(1-x\right)=\left(1-y\right)\times 3\left(4-x\right)$$

To find the opposite of 1+y, find the opposite of each term.

$$\left(-1-y\right)\left(1-x\right)=\left(1-y\right)\times 3\left(4-x\right)$$

Use the distributive property to multiply -1-y by 1-x.

$$-1+x-y+yx=\left(1-y\right)\times 3\left(4-x\right)$$

Use the distributive property to multiply 1-y by 3.

$$-1+x-y+yx=\left(3-3y\right)\left(4-x\right)$$

Use the distributive property to multiply 3-3y by 4-x.

$$-1+x-y+yx=12-3x-12y+3yx$$

Add 3x to both sides.

$$-1+x-y+yx+3x=12-12y+3yx$$

Combine x and 3x to get 4x.

$$-1+4x-y+yx=12-12y+3yx$$

Subtract 3yx from both sides.

$$-1+4x-y+yx-3yx=12-12y$$

Combine yx and -3yx to get -2yx.

$$-1+4x-y-2yx=12-12y$$

Add 1 to both sides.

$$4x-y-2yx=12-12y+1$$

Add 12 and 1 to get 13.

$$4x-y-2yx=13-12y$$

Add y to both sides.

$$4x-2yx=13-12y+y$$

Combine -12y and y to get -11y.

$$4x-2yx=13-11y$$

Combine all terms containing x.

$$\left(4-2y\right)x=13-11y$$

Divide both sides by -2y+4.

$$\frac{\left(4-2y\right)x}{4-2y}=\frac{13-11y}{4-2y}$$

Dividing by -2y+4 undoes the multiplication by -2y+4.

$$x=\frac{13-11y}{4-2y}$$

Divide 13-11y by -2y+4.

$$x=\frac{13-11y}{2\left(2-y\right)}$$

Solve for y

$$y=-\frac{4x-13}{11-2x}$$

$$x\neq 1\text{ and }x\neq \frac{11}{2}\text{ and }x\neq 4$$

Steps for Solving Linear Equation

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

$$-\left(1+y\right)\left(1-x\right)=\left(1-y\right)\times 3\left(4-x\right)$$

To find the opposite of 1+y, find the opposite of each term.

$$\left(-1-y\right)\left(1-x\right)=\left(1-y\right)\times 3\left(4-x\right)$$

Use the distributive property to multiply -1-y by 1-x.

$$-1+x-y+yx=\left(1-y\right)\times 3\left(4-x\right)$$

Use the distributive property to multiply 1-y by 3.

$$-1+x-y+yx=\left(3-3y\right)\left(4-x\right)$$

Use the distributive property to multiply 3-3y by 4-x.

$$-1+x-y+yx=12-3x-12y+3yx$$

Add 12y to both sides.

$$-1+x-y+yx+12y=12-3x+3yx$$

Combine -y and 12y to get 11y.

$$-1+x+11y+yx=12-3x+3yx$$

Subtract 3yx from both sides.

$$-1+x+11y+yx-3yx=12-3x$$

Combine yx and -3yx to get -2yx.

$$-1+x+11y-2yx=12-3x$$

Add 1 to both sides.

$$x+11y-2yx=12-3x+1$$

Add 12 and 1 to get 13.

$$x+11y-2yx=13-3x$$

Subtract x from both sides.

$$11y-2yx=13-3x-x$$

Combine -3x and -x to get -4x.

$$11y-2yx=13-4x$$

Combine all terms containing y.

$$\left(11-2x\right)y=13-4x$$

Divide both sides by -2x+11.

$$\frac{\left(11-2x\right)y}{11-2x}=\frac{13-4x}{11-2x}$$

Dividing by -2x+11 undoes the multiplication by -2x+11.

$$y=\frac{13-4x}{11-2x}$$

Variable y cannot be equal to any of the values -1,1.

$$y=\frac{13-4x}{11-2x}\text{, }y\neq -1\text{ and }y\neq 1$$