SOLUTION: Given the system 2x+5y=1 and 3x+ky=4, find k such that this system has no solution.

Question 472697: Given the system 2x+5y=1 and 3x+ky=4, find k such that this system has no solution.

Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Two linear equations will not intersect if they are parallel. The slope of the first line is -2/5 (simply solve for y), so we want the slope of the line 3x+ky = 4 to also equal -2/5.

Solving for y in the second equation we get y = (-3/k)x + (stuff), we set -3/k = -2/5 to get k = 15/2.

(The "stuff" indicates that it is not important so it is useless trying to find what its y-intercept is. It is only problematic when the y-intercepts of both equations are equal...in which they're not in this case)
RELATED QUESTIONS
Find the value(s) of the constant k such that the system of linear equations: 9x + ky =... (answered by htmentor,ikleyn)

Find K if the given system of equations has infinite no of solutions. 2x+ky=1+2y and... (answered by stanbon)

what is k if the following system of equations has a unique solution: 2x+(k-1)y=6... (answered by stanbon)

The value of k for which the system the equations x+5y=0, and 3x+ky=0 has nonzero... (answered by ikleyn)

Hi, I'm Michele and I could really use someones help on my problem. I will be greatful... (answered by stanbon)

determine the value of k for which the system of linear equations has no solution:... (answered by vleith)

i need all the steps to solving this linear equation, thank you. determine the value... (answered by venugopalramana)

Please help me solve this question. Find the value(s) of the constant k such that the... (answered by Boreal)

Please help me solve this problem. Determine all the value of k such that the... (answered by ikleyn)