Question

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?

Answer 1

Given:

The system of equations:

`x-3y=9`

`(1)/(5)x-2y=-1`

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,

`x-3y=9` ...(i)

`(1)/(5)x-2y=-1` ...(ii)

The coefficient of x in (i) and (ii) are 1 and
`(1)/(5)` 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
`(1)/(5)` into -1. It is possible if we multiply the equation (ii) by -5.

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

`-x+10y=5` ...(iii)

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

`7y=14`

Here, x is eliminated.

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