Section 2 Category 10

Example 1 - mental math

It can be observed that in the top equation the value of b is 3 times of the bottom equation. Since the system has infinitely many solutions, the vales of a and c in the top equation must also be 3 times of the bottom equation (this will result in the same ratios of a, b, and c).

Hence, a = 12 and c = 3.


Example 2 - mental math for those good with dividing fractions

It can be observed that in the top equation the value of c is 12 times of the bottom equation. Since the system has infinitely many solutions, the values of a and b in the top equation must also be 12 times of the bottom equation (this will result in the same ratios of a, b, and c).

Hence, a = 4 and b = 3.