Find the value of c such that the system of equations -6x-4y=13 and 15x+cy=-14 doesn't have a sol.?

Question

Find the value of c such that the system of equations -6x-4y=13 and 15x+cy=-14 doesn't have a sol.?

Answer 1

2 straight lines (in slope and y-intercept form) on graph

y = mx + p

y = m1x + p1

will have no solution, if slopes are same (parallel) when they are not coincident, i.e.

no solution > if m = m1 but p NOT = p1

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infinite solutions >>  m = m1 and p = p1

coincident lines

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y = [- 6/4] x + [-13/4] >>>>>>>> m = [ -3/2], p = - 13/4

y = [- 15/c] x + [-14/c] >>>>>>>> m1 = [ -15/c], p1 = - 14/c

m = m1 gives

- 15/c = -3/2

c = 30/3 = 10

c = 10 >>>>>>>>>>>>>>

with this p NOT = p

so no solution

2 distinct parallel lines, which never meet > so no solution