Question 656167: Determine the value of k for which system of linear equation has no solution.
2x-y=3
4x+ky=5 Found 3 solutions by MathLover1, Edwin McCravy, chandrak:Answer by MathLover1(20850) (Show Source):
You can put this solution on YOUR website! No solution means the lines are .
The left hand sides are multiples of each other.
Find the multiplier so that,
Solve for the and terms on both sides.
......->... ...->... ...->...
2x - y = 3
4x + ky = 5
Solve by substitution, solve the first for y
2x - y = 3
-y = 3 - 2x
y = -3 + 2x
Substitute in the second equation:
4x + k(-3 + 2x) = 5
4x - 3k + 2kx = 5
4x + 2kx = 5 + 3k
x(4 + 2k) = 5 + 3k
x =
This cannot be a solution if the denominator = 0,
so we set the denominator = 0
4+2k = 0
2k = -4
k = -2
So if k = -2, there is no solution.
Edwin
You can put this solution on YOUR website! Solution for a system of linear equations is a common point in both equations
that is the point where they intersect.
Two lines always intersect unless they are parallel lines.
So if they are parallel lines there is no solution
parallel lines have same slope
y = mx + c1 ------slope m
y = mx + c2 ------slope m
Represent the given equations in the slope intercept form
Equation 1
2x-y = 3
y = 2x-3 slope = 2
Equation 2
4x+ky = 5
ky = -4x + 5
y = -4x/k + 5/k
for the slope to be the same as equation 1 that is 2
-4/k = 2
k = -2
so if k = -2 both equations have same slope and they are parallel
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