66.9k views
11 votes
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?

User Bradreaves
by
7.5k points

1 Answer

7 votes

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.

User Dirk McQuickly
by
7.9k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories