# Solve by Substitution y=|x^2-3x+1| , y=x-1 ,
Eliminate the equal sides of each equation and combine.
Solve for .
Remove the absolute value term. This creates a on the right side of the equation because .
Set up the positive portion of the solution.
Solve the first equation for .
Move all terms containing to the left side of the equation.
Subtract from both sides of the equation.
Subtract from .
Move all terms to the left side of the equation and simplify.
Add to both sides of the equation.
Use the quadratic formula to find the solutions.
Substitute the values , , and into the quadratic formula and solve for .
Simplify.
Simplify the numerator.
Raise to the power of .
Multiply by .
Multiply by .
Subtract from .
Rewrite as .
Factor out of .
Rewrite as .
Pull terms out from under the radical.
Multiply by .
Simplify .
Simplify the expression to solve for the portion of the .
Simplify the numerator.
Raise to the power of .
Multiply by .
Multiply by .
Subtract from .
Rewrite as .
Factor out of .
Rewrite as .
Pull terms out from under the radical.
Multiply by .
Simplify .
Change the to .
Simplify the expression to solve for the portion of the .
Simplify the numerator.
Raise to the power of .
Multiply by .
Multiply by .
Subtract from .
Rewrite as .
Factor out of .
Rewrite as .
Pull terms out from under the radical.
Multiply by .
Simplify .
Change the to .
The final answer is the combination of both solutions.
Set up the negative portion of the solution.
Solve the second equation for .
Simplify .
Rewrite.
Apply the distributive property.
Multiply by .
Move all terms containing to the left side of the equation.
Add to both sides of the equation.
Subtract from both sides of the equation.
Combine the opposite terms in .
Subtract from .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Set equal to .
Set equal to and solve for .
Set equal to .
Add to both sides of the equation.
The final solution is all the values that make true.
The solution to the equation includes both the positive and negative portions of the solution.
Exclude the solutions that do not make true.
Evaluate when .
Substitute for .
Substitute for in and solve for .
Remove parentheses.
Remove parentheses.
Subtract from .
Evaluate when .
Substitute for .
Substitute for in and solve for .
Remove parentheses.
Remove parentheses.
Subtract from .
The solution to the system is the complete set of ordered pairs that are valid solutions.
The result can be shown in multiple forms.
Point Form:
Equation Form:
Solve by Substitution y=|x^2-3x+1| , y=x-1     