Question 676683: Can you help me with this question? I need it answer by today.
For what values of k is the system of equations independent?
4x + y = 4
kx + y = 6
Write the first equation in slope-intercept form. Subtract
4x
from each side of the equation
4x + y = 4.
y = + 4
art (b)
x + 2y = 5
kx + 3y = 3
Part (c)
2x + ky = 7
x + 2y = 4
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! For what values of k is the system of equations independent?
4x + y = 4
kx + y = 6
The 2 eqns are independent for all values of k.
If k = 4, they're inconsistent.
--------------------------------
Write the first equation in slope-intercept form.
Subtract 4x
from each side of the equation
4x + y = 4.
y = + 4 ***************** y = 4 - 4x
Or y = -4x + 4 is the form y = mx + b
====================================
art (b)
x + 2y = 5
kx + 3y = 3
Same as the 1st question, but
if k = 1.5 the eqns are inconsistent.
--------------------------
x + 2y = 5
2y = -x + 5
y = (-1/2)x + 5/2
======================
Part (c)
2x + ky = 7
x + 2y = 4
Same, if k = 4 --> inconsistent
2x + ky = 7
ky = -2x + 7
y = (-2/k)x + 7/k
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