Compare your answers

 

  1. State a preferable method for solving each of the following systems. Justify your choice.

    Choices and explanations will vary. Samples are shown.

    1.   «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»1«/mn»«/math»
        «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»y«/mi»«mo»=«/mo»«mi»x«/mi»«mo»-«/mo»«mn»6«/mn»«/math»

      Substitution will work well with this system because x, in the first equation, is already isolated.

    2.   «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»y«/mi»«mo»=«/mo»«mn»5«/mn»«mo».«/mo»«mn»1«/mn»«mi»x«/mi»«mo»-«/mo»«mn»7«/mn»«/math»
        «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»y«/mi»«mo»=«/mo»«mn»3«/mn»«mo».«/mo»«mn»9«/mn»«mi»x«/mi»«mo»+«/mo»«mn»2«/mn»«mo».«/mo»«mn»2«/mn»«/math»

      3. Graphing using technology will work well for this system because both equations are written in slope-intercept form, which is easy to enter into a graphing calculator.

    3.   «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»3«/mn»«mi»x«/mi»«mo»+«/mo»«mn»5«/mn»«mi»y«/mi»«mo»-«/mo»«mn»1«/mn»«mo»=«/mo»«mn»0«/mn»«/math»
        «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»6«/mn»«mi»x«/mi»«mo»+«/mo»«mi»y«/mi»«mo»+«/mo»«mn»13«/mn»«mo»=«/mo»«mn»0«/mn»«/math»

      Elimination will work well for this system because the equations are in the same format, and multiplying the first equation by 2 will make the x-coefficients the same.

  2. Solve «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»y«/mi»«mo»=«/mo»«mn»3«/mn»«mi»x«/mi»«mo»-«/mo»«mn»4«/mn»«/math» and «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»y«/mi»«mo»=«/mo»«mn»2«/mn»«mi»x«/mi»«mo»+«/mo»«mn»2«/mn»«/math» using an algebraic method (substitution or elimination). Verify your work by graphing with technology.



    The solution is (6, 14).
    Verify the solution.