Another system of equations question

[mz985]

Hi guys,

Here is the problem:

4x + 3y= 20
2x + y = 7

I have to find the value of y

Was wondering if this problems answer (6)

Now was one of the ways the answer to this problem was found is by taking both the 20 and 7 and multiplying 7 by -2 to get -14 and subtract from 20 to get 6? I'm trying to figure out was done exactly to arrive at this answer but if thats the case I'm not sure how the x was lost and I think its negative since we are trying to find y and eliminated the 2x by making it negative.

 

[HallsofIvy]

Hi guys,

Here is the problem:

4x + 3y= 20
2x + y = 7

I have to find the value of y

Was wondering if this problems answer (6)

Now was one of the ways the answer to this problem was found is by taking both the 20 and 7 and multiplying 7 by -2 to get -14 and subtract from 20 to get 6?

That makes no sense to me because you give no reason for doing those things. You make it sound as if you were just combing numbers at random!

You have two equations and you want to solve for y so you want to eliminate x. If the equation had "ax" and "ax", that is with the same coefficient, we could just subtract: ax- ax=0. Since one equation has "4x" and the other has "2x", we can get the same coefficient by multiplying the second equation by 2:
2(2x+ y= 7) gives 4x+ 2y= 14. Now we have 4x+ 3y= 20 and 4x+ 2y= 14. Subtracting one equation from the other gives (4x- 4x)+ (3y- 2y)= 20- 14 or just y= 6.

Another way to do this problem is to solve equation 2 for y, y= 7- 2x, and then replace the "y" in the first equation by that: 4x+ 3(7- 2x)= 4x+ 21- 6x= -2x+ 21= 20 so that -2x= -1 and x= 1/2. Since y= 7- 2x, y= 7- 2(1/2)= 7- 1= 6.

I'm trying to figure out was done exactly to arrive at this answer but if thats the case I'm not sure how the x was lost and I think its negative since we are trying to find y and eliminated the 2x by making it negative.

Again, that makes no sense. Why would "making 2x negative" eliminate it? This is a criticism more of your grammar than algebra but how you explain what you are doing is just as important as doing it. Say what you mean!