Section 2 Category 9

Example 1 - mental math

It can be observed that in the top equation the value of b is 4 times of the bottom equation. For the equation to have no solution, the value of a in the top equation must also be 4 times of the bottom equation (this will result in the same ratios of a and b).

Since a = 1 in the bottom equation, it must be 4 in the top equation. Hence, 2n = 4 - -> n = 2.


Example 2 - mental math

It can be observed that in the top equation the values of a and b are one-third of the bottom equation. For the system to have no solution, the value of c in the top equation cannot be one-third of the bottom equation. Hence k = c cannot be 1.