Given:
The system of equations:
[tex]x-3y=9[/tex]
[tex]\dfrac{1}{5}x-2y=-1[/tex]
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,
[tex]x-3y=9[/tex] ...(i)
[tex]\dfrac{1}{5}x-2y=-1[/tex] ...(ii)
The coefficient of x in (i) and (ii) are 1 and [tex]\dfrac{1}{5}[/tex] 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 [tex]\dfrac{1}{5}[/tex] into -1. It is possible if we multiply the equation (ii) by -5.
On multiplying equation (ii) by -5, we get
[tex]-x+10y=5[/tex] ...(iii)
On adding (i) and (iii), we get
[tex]7y=14[/tex]
Here, x is eliminated.
Therefore, the number -5 can be multiplied by the second equation to eliminate the x-variable.
