Question

Which constants can be multiplied by the equations so one variable will be eliminated when the systems are added together?

5x + 13y = 232
12x + 7y = 218

Answer 1

You can start off by distributing the x-variables and using the LCM of 5 and 12

5 = 5x1
12= 2x2x3

LCM: 1x2x2x3x5= 60

We could also determine the LCM of 13 and 7 (y-variables), since they are both prime numbers.

13x7= 91

The LCM is 91.

Answer 2

The first equation can be multiplied by –12 and the second equation by 5 to eliminate x.