Consider the system of equations. x-3y = 9
1/5 x - 2y = -1
Which number can be multiplied by the second equation to eliminate the x-variable when the equations are added
together?

Given:

The system of equations:

To find:

The number that can be multiplied by the second equation to eliminate the x-variable when the equations are added together.

Solution:

We have,

                       ...(i)

      ...(ii)

The coefficient of x in (i) and (ii) are 1 and respectively.

To eliminate the variable x by adding the equations, we need the coefficients of x as the additive inverse of each other, i.e, a and -a So, a+(-a)=0.

It means, we have to convert into -1. It is possible if we multiply the equation (ii) by -5.

On multiplying equation (ii) by -5, we get

      ...(iii)

On adding (i) and (iii), we get

Here, x is eliminated.

Therefore, the number -5 can be multiplied by the second equation to eliminate the x-variable.

inverse operation of addition