Answers

  • Brainly User
2016-01-29T13:56:41+08:00
Transform the equations to slope-intercept form, y = mx + b; m=slope

1) For parallel equations, the slopes must be equal.
    Equation 1:
    5x - 6y = 8
    - 6y = - 5x + 8
    - 6y/-6  = -5x/-6 + 8/-6
    y = 5x/6 - 4/3
    m = 5/6
   
    Equation 2:
    kx - 3y = 5
    - 3y = -kx + 5
    - 3y/-3  = -kx/-3 + 5/-3
    y = kx/3 - 5/3
    m = k/3    
   
   Solve for k:
    m = 5/6
    k/3 = 5/6
    6k = (3) (5)
    6k = 15
    6k/6 = 15/6
    k = 5/2
  
    Therefore, Equation 2 is:
     5x/2 - 3y = 5     LCD: 2
     2 (5x/2 - 3y = 5)2
     5x - 6y = 10
     
     Slope-intercept form:
     -6y = -5x + 10
     -6y/-6 = -5x/-6 + 10/-6
     y = 5x/6 - 5/3
     m = 5/6   (True)
     
2)  For perpendicular equations, the product of the slopes of the two equations is -1.  
     Equation 1:
     m = 5/6
    
     Equation 2:
     m = -6/5

    Solve for k:
    k/3 = -6/5
    5k = (3) (-6)
    5k = -18
    5k/5 = -18/5
    k = -18/5

    Therefore, to make the equations perpendicular, Equation 2 is:
     kx - 3y = 5
     -18x/5 - 3y = 5       LCD: 5
     5 (-18x/5 - 3y = 5) 5
     -18x - 15y = 25
     
      Slope-intercept form:
      -15y = 18x + 25
      -15y/-15 = 18x/-15 + 25/-15
       y = -6x/5 - 5/3
       m = -6/5    (True)
     
ANSWER:  To make the equations parallel, k = 5/2.
                    To make the equations perpendicular, k = -18/5
     
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