Solve 50-x/45-y=x-100/y-60

$$\frac{ 50-x }{ 45-y } = \frac{ x-100 }{ y-60 }$$

Solve for x

$$x=\frac{10\left(y-30\right)}{3}$$

$$y\neq 45\text{ and }y\neq 60$$

Steps for Solving Linear Equation

Multiply both sides of the equation by \left(y-60\right)\left(y-45\right), the least common multiple of 45-y,y-60.

$$\left(60-y\right)\left(50-x\right)=\left(y-45\right)\left(x-100\right)$$

Use the distributive property to multiply 60-y by 50-x.

$$3000-60x-50y+yx=\left(y-45\right)\left(x-100\right)$$

Use the distributive property to multiply y-45 by x-100.

$$3000-60x-50y+yx=yx-100y-45x+4500$$

Subtract yx from both sides.

$$3000-60x-50y+yx-yx=-100y-45x+4500$$

Combine yx and -yx to get 0.

$$3000-60x-50y=-100y-45x+4500$$

Add 45x to both sides.

$$3000-60x-50y+45x=-100y+4500$$

Combine -60x and 45x to get -15x.

$$3000-15x-50y=-100y+4500$$

Subtract 3000 from both sides.

$$-15x-50y=-100y+4500-3000$$

Subtract 3000 from 4500 to get 1500.

$$-15x-50y=-100y+1500$$

Add 50y to both sides.

$$-15x=-100y+1500+50y$$

Combine -100y and 50y to get -50y.

$$-15x=-50y+1500$$

The equation is in standard form.

$$-15x=1500-50y$$

Divide both sides by -15.

$$\frac{-15x}{-15}=\frac{1500-50y}{-15}$$

Dividing by -15 undoes the multiplication by -15.

$$x=\frac{1500-50y}{-15}$$

Divide -50y+1500 by -15.

$$x=\frac{10y}{3}-100$$

Solve for y

$$y=\frac{3\left(x+100\right)}{10}$$

$$x\neq 50\text{ and }x\neq 100$$

Steps for Solving Linear Equation

Variable y cannot be equal to any of the values 45,60 since division by zero is not defined. Multiply both sides of the equation by \left(y-60\right)\left(y-45\right), the least common multiple of 45-y,y-60.

$$\left(60-y\right)\left(50-x\right)=\left(y-45\right)\left(x-100\right)$$

Use the distributive property to multiply 60-y by 50-x.

$$3000-60x-50y+yx=\left(y-45\right)\left(x-100\right)$$

Use the distributive property to multiply y-45 by x-100.

$$3000-60x-50y+yx=yx-100y-45x+4500$$

Subtract yx from both sides.

$$3000-60x-50y+yx-yx=-100y-45x+4500$$

Combine yx and -yx to get 0.

$$3000-60x-50y=-100y-45x+4500$$

Add 100y to both sides.

$$3000-60x-50y+100y=-45x+4500$$

Combine -50y and 100y to get 50y.

$$3000-60x+50y=-45x+4500$$

Subtract 3000 from both sides.

$$-60x+50y=-45x+4500-3000$$

Subtract 3000 from 4500 to get 1500.

$$-60x+50y=-45x+1500$$

Add 60x to both sides.

$$50y=-45x+1500+60x$$

Combine -45x and 60x to get 15x.

$$50y=15x+1500$$

Divide both sides by 50.

$$\frac{50y}{50}=\frac{15x+1500}{50}$$

Dividing by 50 undoes the multiplication by 50.

$$y=\frac{15x+1500}{50}$$

Divide 1500+15x by 50.

$$y=\frac{3x}{10}+30$$

Variable y cannot be equal to any of the values 45,60.

$$y=\frac{3x}{10}+30\text{, }y\neq 45\text{ and }y\neq 60$$