help w/ solving system: 4x + 3y = 9, 2x - 2y = 8

T

thepcnerd

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Dec 4, 2006
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On this problem, I'm solving for x and y. Here's what I have so far:

The system:

. . .4x + 3y = 9
. . .2x - 2y = 8

Adding the two equations:

. . .4x + (2x) + 3y + (-2y) = 9 + 8
. . .6x + y = 17
. . .-6. . . . . .-6
. . .y(1) = 11
. . .11/1=1
. . .1*11=11

...so y = 1. Now for x:

. . .4x + 3(1) = 9
. . .4x + 3 = 9
. . . . .+3. . .+3
. . .4x = 12
. . .12/4 = 3
. . .3*4=12

...so y=3

. . .2x - 2(1) = 8
. . .2x - 2 = 8
. . . . .-2. . . -2
. . .2x = 6
. . .6/2=3
. . .3*2=6

...so y = 3. My solution is (x, y) = (3, 1). But the book says the answer is (x, y) = (3, -1). What am I doing wrong?

Thank you!
 
thepcnerd said:
Adding the two equations:

. . .4x + (2x) + 3y + (-2y) = 9 + 8
. . .6x + y = 17
Click to expand...
Since nothing is set to cancel, adding the equations at this point is not helpful, as you can see in your result: you still have an equation with two variables.

In your next step, where you subtract 6 from either side, note that, since "6" and "6x" are unlike terms, nothing combines or cancels with the variable terms. You are left with:

. . . . .6x + y = 17
. . . . .6x + y - 6 = 17 - 6
. . . . .6x + y - 6 = 11

This doesn't get you any nearer a solution.

I couldn't make heads or tails of what came after this point....

To solve the system by addition/elimination, you need to multiply one or both of the equations by something that will cause a cancellation. I would suggest multiplying the second equation by -2, to get:

. . . . ..4x + 3y = . .9
. . . . .-4x + 4y = -16

Then add down, and solve the resulting linear equation for the value of y.

Eliz.
 
thepcnerd said:
where dp we get -2?
Click to expand...
You have a +4x and a +2x. What would you multiply, and by what, to get those terms to cancel out?

Eliz.
 
lol

lol, ty i never had a great algebra class or teachers for that matter i graduated almost failing algerbra and not understanding any of it, im just now trying to clep/stufy for acuplacer for college so i can get on with my education. so thats why i dont understand any of this stuff, its ard to find good books or sites that can explain it all in depth and through so i know how to work the many diff combos, etc... thanks again and in advance
 
Re: lol

thepcnerd said:
lol, ty i never had a great algebra class or teachers for that matter i graduated almost failing algerbra and not understanding any of it, im just now trying to clep/stufy for acuplacer for college so i can get on with my education. so thats why i dont understand any of this stuff, its ard to find good books or sites that can explain it all in depth and through so i know how to work the many diff combos, etc... thanks again and in advance
Click to expand...
You graduated what? High School?

When did you "graduate"?

Why were your teachers "not great"? Did the whole class think so?
 
yeah

2004 yeah most peps thought so, they were the king they would do one problem on the board through the materail at you, say do it and that was it. They would snarl their faces and get all cocky like if u would of went to the desk to get help on a prob u didnt understand, but this came natural to most people in the class, some friends tried showing me, i just couldnt get t down, and now im forced to if i want to further my education....
 
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