5x+7y=31 2x+4y=16 which of the following systems could be used to solve the given system of equations by the addition method? 10x + 14y = 31 and -10x - 20y = 16 10x + 14y = 62 and 10x + 20y = 32 -10x - 14y = -62 and 10x + 20y = 80

Equation 1: 
Equation 2: 

We can either use the 'elimination' method or the 'substitution' method to solve this simultaneous equation.

In some cases one method is easier to use than the other. For this one, it would be easier to use the elimination method

We need to eliminate either the 'x' or the 'y' to begin with. Say we want to eliminate the 'x' terms, then the next step is to make the constant the same

Equation 1: the constant of 'x' is 5
Equation 2: the constant of 'x' is 2

To make the two constants the same, think of common multiple. The lowest common multiple for 5 and 2 is 10

Equation 1:  Multiply all terms by 2 to achieve 10x
Equation 2: Multiply all terms by 5 to achieve 10x

Equation 1: 
Equation 2: 

Once the constant of 'x' is the same, then we can start the elimination process. Since our aim is to eliminate, one of the 'x' need to be in negative form. We can either multiply Equation 1 or Equation 2 by (-1)

Equation 1: -10x - 14y = -62
Equation 2: 10x + 20y = 80

Hence the correct answer is: Third option