Solve frac{1-x_{0}}{1-x_{0}}=frac{y-y_{0}}{5-y_{0}}

$$\frac { 1 - x _ { 0 } } { 1 - x _ { 0 } } = \frac { y - y _ { 0 } } { 5 - y _ { 0 } }$$

Solve for x_0

$$x_{0}\neq 1$$

$$y=5\text{ and }y_{0}\neq 5$$

Steps for Solving Linear Equation

Variable x_{0} cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by \left(x_{0}-1\right)\left(y_{0}-5\right), the least common multiple of 1-x_{0},5-y_{0}.

$$\left(5-y_{0}\right)\left(1-x_{0}\right)=\left(1-x_{0}\right)\left(y-y_{0}\right)$$

Use the distributive property to multiply 5-y_{0} by 1-x_{0}.

$$5-5x_{0}-y_{0}+y_{0}x_{0}=\left(1-x_{0}\right)\left(y-y_{0}\right)$$

Use the distributive property to multiply 1-x_{0} by y-y_{0}.

$$5-5x_{0}-y_{0}+y_{0}x_{0}=y-y_{0}-x_{0}y+y_{0}x_{0}$$

Add x_{0}y to both sides.

$$5-5x_{0}-y_{0}+y_{0}x_{0}+x_{0}y=y-y_{0}+y_{0}x_{0}$$

Subtract y_{0}x_{0} from both sides.

$$5-5x_{0}-y_{0}+y_{0}x_{0}+x_{0}y-y_{0}x_{0}=y-y_{0}$$

Combine y_{0}x_{0} and -y_{0}x_{0} to get 0.

$$5-5x_{0}-y_{0}+x_{0}y=y-y_{0}$$

Subtract 5 from both sides.

$$-5x_{0}-y_{0}+x_{0}y=y-y_{0}-5$$

Add y_{0} to both sides.

$$-5x_{0}+x_{0}y=y-y_{0}-5+y_{0}$$

Combine -y_{0} and y_{0} to get 0.

$$-5x_{0}+x_{0}y=y-5$$

Combine all terms containing x_{0}.

$$\left(-5+y\right)x_{0}=y-5$$

The equation is in standard form.

$$\left(y-5\right)x_{0}=y-5$$

Divide both sides by y-5.

$$\frac{\left(y-5\right)x_{0}}{y-5}=\frac{y-5}{y-5}$$

Dividing by y-5 undoes the multiplication by y-5.

$$x_{0}=\frac{y-5}{y-5}$$

Divide y-5 by y-5.

$$x_{0}=1$$

Variable x_{0} cannot be equal to 1.

$$x_{0}\in \emptyset$$

Solve for y

$$y=5$$

$$x_{0}\neq 1\text{ and }y_{0}\neq 5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by \left(x_{0}-1\right)\left(y_{0}-5\right), the least common multiple of 1-x_{0},5-y_{0}.

$$\left(5-y_{0}\right)\left(1-x_{0}\right)=\left(1-x_{0}\right)\left(y-y_{0}\right)$$

Use the distributive property to multiply 5-y_{0} by 1-x_{0}.

$$5-5x_{0}-y_{0}+y_{0}x_{0}=\left(1-x_{0}\right)\left(y-y_{0}\right)$$

Use the distributive property to multiply 1-x_{0} by y-y_{0}.

$$5-5x_{0}-y_{0}+y_{0}x_{0}=y-y_{0}-x_{0}y+y_{0}x_{0}$$

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

$$y-y_{0}-x_{0}y+y_{0}x_{0}=5-5x_{0}-y_{0}+y_{0}x_{0}$$

Add y_{0} to both sides.

$$y-x_{0}y+y_{0}x_{0}=5-5x_{0}-y_{0}+y_{0}x_{0}+y_{0}$$

Combine -y_{0} and y_{0} to get 0.

$$y-x_{0}y+y_{0}x_{0}=5-5x_{0}+y_{0}x_{0}$$

Subtract y_{0}x_{0} from both sides.

$$y-x_{0}y=5-5x_{0}+y_{0}x_{0}-y_{0}x_{0}$$

Combine y_{0}x_{0} and -y_{0}x_{0} to get 0.

$$y-x_{0}y=5-5x_{0}$$

Combine all terms containing y.

$$\left(1-x_{0}\right)y=5-5x_{0}$$

Divide both sides by 1-x_{0}.

$$\frac{\left(1-x_{0}\right)y}{1-x_{0}}=\frac{5-5x_{0}}{1-x_{0}}$$

Dividing by 1-x_{0} undoes the multiplication by 1-x_{0}.

$$y=\frac{5-5x_{0}}{1-x_{0}}$$

Divide 5-5x_{0} by 1-x_{0}.

$$y=5$$