SOLUTION: Find the approximate solution of this system of equations. y = |x^2 − 3x + 1| y = x − 1 a. (1, 0) b. (4.5, 3.5) c. (2, 1) d. (3.4, 2.3) e. (0.6, -0.4)

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Find the approximate solution of this system of equations. y = |x^2 − 3x + 1| y = x − 1 a. (1, 0) b. (4.5, 3.5) c. (2, 1) d. (3.4, 2.3) e. (0.6, -0.4)      Log On


   

Question 971646: Find the approximate solution of this system of equations.
y = |x^2 − 3x + 1|
y = x − 1

a. (1, 0)
b. (4.5, 3.5)
c. (2, 1)
d. (3.4, 2.3)
e. (0.6, -0.4)
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The absolute value equation has two critical values for x, the roots.
%283%2B-+sqrt%285%29%29%2F2; to the left and right of the roots the equation is y=x%5E2-3x%2B1 and between them is y=-x%5E2%2B3x-1. You just want to find in which interval of x does the line y=x-1 intersect the absolute value equation.

Try testing for the middle interval first.
system%28y=x-1%2Cy=-x%5E2%2B3x-1%29
x-1=-x%5E2%2B3x-1
**-x%5E2%2B3x-x=0
x%5E2-3x%2Bx=0
x%5E2-2x=0
x=0 or x=1/2
(**this must be a mistake.)
Where is each of these two solutions? To left of the smaller critical value? To the right of the greater critical value? Between the two critical values?

Solution to the problem not finished, but you should understand this strategy.



graph%28300%2C300%2C-3%2C3%2C-3%2C3%2Cx-1%2Cabs%28x%5E2-3x%2B1%29%29

Once the mistake is corrected, you should find as shown in the graph, the solution is point (2,1).