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