Chapter 9.6, Problem 5E

To determine

To solve the system of equation by graphing.

  $y=-x^2+x-1$

  $y=x-1$

Answer to Problem 5E

There is one solutions which is $(0,-1)$

Explanation of Solution

Given information:

The system of equation

  $y=-x^2+x-1$

  $y=x-1$

Calculation:

The system of equation

  $y=-x^2+x-1$

  $y=x-1$

Option(A) is the graph of system of equation

  

The graph of system of equation intersecting at $(0,-1)$

Put each solution in the both original equations to check that the values make both equations true

  $y=-x^2+x-1$ Original equation $y=x-1$

  $-1=-0^2+0-1$

  $x=0,y=-1$

  $-1=0-1$

  $-1=0+0-1$ Simplify $-1=-1$

  $-1=-1$ true Simplify $-1=-1$ true

There is one solutions which is $(0,-1)$