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For what value of k will the system be inconsistent?

1. y=kx+2
y= -2x-3

2. 4x+y=3
kx-2y=6

3. 2x+5y= -7
x-ky=2

4. x/2 + y/5 =1
2y =kx+6

Sagot :

A.) For the system to be inconsistent, the slopes must be the same.  
B.) Convert the equations to y = mx + b (slope-intercept form).

1)  y = -2x - 3          
    m (slope) = -2
   
    y = kx + 2
    k = -2
    To check:
    y = -2x + 2
    m = -2

2)  4x + y = 3
    y = -4x + 3
    m = -4
   
    kx - 2y = 6
    -2y = -kx + 6
    k = -8
   To check:
    kx - 2y = 6
    -8x - 2y = 6
    - 2y = 8x + 6
     -2y/-2 = 8x/-2 + 6/-2
      y = -4x - 3
      m = -4

3)  2x + 5y = -7
    5y = -2x - 7
    5y/5 = -2x/5 - 7/5
    y = -2x/5 - 7/5
    m = -2/5
   
   x - ky = 2
   -ky = -x + 2
    k = -5/2
   
     To check:
    x - (-5/2)y = 2
    x + (5/2)y = 2
    (5/2)y = -x + 2
     (2/5) [(5/2)y = -x + 2] (2/5)
     y = (-2/5)x +4/5
     m = -2/5 

4.)  x/2 + y/5 = 1
     LCD: (5)(2)
     (5)(2) (x/2) + (5)(2)(y/5) = (5)(2)(1)
      5x + 2y = 10
      2y = -5x + 10
      2y/2 = -5x/2 + 10/2
      y = (-5/2)x + 5
      m = -5/2
   
      2y = kx + 6
      k = -5
     To check: 
      2y = -5x + 6
      2y/2 = -5x/2 + 6/2
      y = -5x/2 + 3
      m = -5/2