B. The Number of Solutions to a System of Linear Equations

Investigation

The relation «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»y«/mi»«mo»=«/mo»«mn»0«/mn»«mo».«/mo»«mn»5«/mn»«mi»x«/mi»«mo»+«/mo»«mn»1«/mn»«/math» is graphed along with three other relations.

  1. Look at the lines «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»y«/mi»«mo»=«/mo»«mn»0«/mn»«mo».«/mo»«mn»5«/mn»«mi»x«/mi»«mo»+«/mo»«mn»1«/mn»«/math» and «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»y«/mi»«mo»=«/mo»«mo»-«/mo»«mn»3«/mn»«mi»x«/mi»«mo»-«/mo»«mn»1«/mn»«/math».

    1. How many points of intersection do the two lines have?


    2. How many solutions does this system of equations have?


  2. Look at the lines «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»y«/mi»«mo»=«/mo»«mn»0«/mn»«mo».«/mo»«mn»5«/mn»«mi»x«/mi»«mo»+«/mo»«mn»1«/mn»«/math» and «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»y«/mi»«mo»=«/mo»«mn»0«/mn»«mo».«/mo»«mn»5«/mn»«mi»x«/mi»«mo»-«/mo»«mn»5«/mn»«/math».

    1. What is the relationship between the two lines?


    2. How many points of intersection do the two lines have?


    3. How many solutions does this system of equations have?

  3. Look at the lines «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»y«/mi»«mo»=«/mo»«mn»0«/mn»«mo».«/mo»«mn»5«/mn»«mi»x«/mi»«mo»+«/mo»«mn»1«/mn»«/math» and «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»-«/mo»«mn»2«/mn»«mi»y«/mi»«mo»+«/mo»«mn»2«/mn»«mo»=«/mo»«mn»0«/mn»«/math».
     

    1. What is the relationship between the two lines?


    2. How many points of intersection do the two lines have?


    3. How many solutions does this system of equations have?