Question

Consider the system of equations.

Answer 1

Given:

The system of equations:

$x-3y=9$

$\dfrac{1}{5}x-2y=-1$

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)

$\dfrac{1}{5}x-2y=-1$       ...(ii)

The coefficient of x in (i) and (ii) are 1 and $\dfrac{1}{5}$ 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 $\dfrac{1}{5}$ 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.