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4 votes
Johanna wrote the system of equations.

4x-3y=1, 5x+4y=9

If the second equation is multiplied by 4, what should the first equation be multiplied by to eliminate the x-variable by addition?

User Kyasbal
by
5.1k points

2 Answers

2 votes

Answer:

-5

Explanation:

User Katrena
by
6.1k points
6 votes

Answer:

-5

Explanation:

If the second equation is multiplied by 4, the coefficient of the x-variable will be 5·4 = 20. To eliminate the x-variable by addition, the first equation needs to be multiplied by a value that will result in an x-coefficient of -20. If that value is k, then we have ...

4k = -20

k = -20/4 = -5

The first equation should be multiplied by -5 to eliminate the x-variable by addition.

_____

Comment on general case

In general, if you have ...

ax +by = c

dx +ey = f

to eliminate the x-variable by addition, you can multiply the second equation by "a" and the first equation by "-d". In the problem above, those numbers are 4 and -5.

User Diane Kaplan
by
5.5k points
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