GMAT MATH - Linear Equations

August 05, 2004

For what values of ‘k’ will the pair of equations 3x + 4y = 12 and kx + 12y = 30 not have a unique solution?

(A)	12
(B)	9
(C)	3
(D)	7.5
(E)	2.5

Correct Choice (B) Answer (9)

Explanatory Answer

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. That is, if they are not parallel lines.

ax + by + c = 0 and dx + ey + g = 0 will not be parallel lines if
In the above question, we need or k should not be equal 9 for the pair of equations to have a unique solution.

In other words, when k = 9, the system of equation will not have any solution as the two lines represented by the equations will be parallel lines.