For what values of 'k' will the pair of equations 3x + 4y = 12 and kx + 12y = 30 NOT have a unique solution?  Choose the most appropriate option.
A) 12	B) 9	C) 3	D) 7.5	E) 2.5
Explanatory Answer   Condition for Unique Solution to Linear Equations   A system of linear equations ax + by + c = 0 and dx + ey + g = 0 will have a unique solution if the two lines represented by the equations ax + by + c = 0 and dx + ey + g = 0 intersect at a point.   i.e., if the two lines are neither parallel nor coincident.   Essentially, the slopes of the two lines should be different.   What does that translate into?   ax + by + c = 0 and dx + ey + g = 0 will intersect at one point if their slopes are different.   Express both the equations in the standardized y = mx + c format, where 'm' is the slope of the line and 'c' is the y-intercept.   ax + by + c = 0 can be written as y = −abx−ca−abx−ca   And dx + ey + g = 0 can be written as y = −dex−ge−dex−ge   Slope of the first line is −ab−ab and that of the second line is −de−de   For a unique solution, the slopes of the lines should be different.   ∴ −ab≠−de−ab≠−de   Or ad≠bead≠be   Condition for the equations to NOT have a unique solution   The slopes should be equal   Or ad=bead=be   Apply the condition in the given equations to find k   In the question given above, a = 3, b = 4, d = k and e = 12.   Therefore, 3k=4123k=412   Or 'k' should be equal to 9 for the pair of equations to NOT have a unique solution.   When k = 9, the system of equations will represent a pair of parallel lines (their y-intercepts are different). So, there will be NO solution.   Answer 9
<result>B</result>
For what values of 'k' will the pair of equations 3x + 4y = 12 and kx + 12y = 30 NOT have a unique solution?