I can't get system of eqns to come out right: 6x=5(x+y+3)-x, 3(x-y)+4y=5(y+x)

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allegansveritatem

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Jan 10, 2018
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I have tried an hour to get this problem. Finally after trying to solve the system with the elimination method, and trying and trying, I graphed the lines. They did meet! Here is the system:
6x=5(x+y+3)-x
3(x-y)+4y=5(y+x)
I simplified this to:
2x-5y=15
3x-4y=5
I multiplied these by -3 and 2 respectively:
-6x+15=-45
6x-8y=10
and got:
7y=-35
y=-2
and I plugged this -2 into the first (reduced) equation:
2x-5(-2)=15
2x=5
x=5/2
This works out for the first equation but not with the second (3x-4y=5).

No matter what I tried I couldn't get these two equations to come right with (5/2, -2) but I was able to graph these lines. They met at (28, 26)--needless to say this pair doesn't work with either equation. What gives here?
 
allegansveritatem said:
I have tried an hour to get this problem. Finally after trying to solve the system with the elimination method, and trying and trying, I graphed the lines. They did meet! Here is the system:
6x=5(x+y+3)-x
3(x-y)+4y=5(y+x)
I simplified this to:
2x-5y=15
3x-4y=5
I multiplied these by -3 and 2 respectively:
-6x+15=-45
6x-8y=10
and got:
7y=-35
y=-2
and I plugged this -2 into the first (reduced) equation:
2x-5(-2)=15
2x=5
x=5/2
This works out for the first equation but not with the second (3x-4y=5).

No matter what I tried I couldn't get these two equations to come right with (5/2, -2) but I was able to graph these lines. They met at (28, 26)--needless to say this pair doesn't work with either equation. What gives here?
Click to expand...

Check every line you write to see if it matches the line above it! You have made several silly arithmetic errors, and some mere typos, I think.

When I pasted your original equations into Desmos, the lines intersect at a fractional point in the fourth quadrant, with small numbers. The simplified equations intersect at a fractional point in the third quadrant. What lines did you graph? How did you graph them?

The key point is that there are so many places to make a silly mistake, you have to do everything very carefully, and check every step.
 
allegansveritatem said:
I have tried an hour to get this problem. Finally after trying to solve the system with the elimination method, and trying and trying, I graphed the lines. They did meet! Here is the system:
6x=5(x+y+3)-x
3(x-y)+4y=5(y+x)
I simplified this to:
2x-5y=15
3x-4y=5
I multiplied these by -3 and 2 respectively:
-6x+15=-45
6x-8y=10
and got:
7y=-35
y=-2
and I plugged this -2 into the first (reduced) equation:
2x-5(-2)=15
2x=5
x=5/2
This works out for the first equation but not with the second (3x-4y=5).

No matter what I tried I couldn't get these two equations to come right with (5/2, -2) but I was able to graph these lines. They met at (28, 26)--needless to say this pair doesn't work with either equation. What gives here?
Click to expand...
See the red above.
You forgot to distribute the 5 to the x, actually you ignored the x completely.
Also 7(-2)\(\displaystyle \neq\) -35. You know that!!!
 
Dr.Peterson said:
Check every line you write to see if it matches the line above it! You have made several silly arithmetic errors, and some mere typos, I think.

When I pasted your original equations into Desmos, the lines intersect at a fractional point in the fourth quadrant, with small numbers. The simplified equations intersect at a fractional point in the third quadrant. What lines did you graph? How did you graph them?

The key point is that there are so many places to make a silly mistake, you have to do everything very carefully, and check every step.
Click to expand...

It is embarrassing to see so many silly mistakes! I must have been off my rocker today! Such stupid stuff.

You ask how I graphed the equations: I used the slope intercept form of the equations...but since one of the equations was wrong, the whole graph was useless.

I am going to work this problem out again tomorrow....it is almost 2 am now...and post the new result. Thanks very much for pointing out my (many) errors. I was perfectly blind to them for some reason. I very often make mistakes when doing the problems at the end of sections but I always stay with a problem until it checks out. Somehow I got really messed up with this one, and, because it was one of the even numbered problems (these are the ones that don't have the solution in the back of the book) I did not have the correct result (very useful in these cases) to work with.
 
Jomo said:
See the red above.
You forgot to distribute the 5 to the x, actually you ignored the x completely.
Also 7(-2)\(\displaystyle \neq\) -35. You know that!!!
Click to expand...

Of course. It's crazy what I did with this problem! I guess the devil made me do it! Thanks.
 
So this morning I returned to this problem. After another false start I at last managed to get it. (-5,-5) is the ordered pair that fits the situation. The more of these problems I work through the easier it gets but still and fairly often I make these small mistakes that blow the game completely. Thanks again to all who helped me peel the scales off my eyes.
 
allegansveritatem said:
So this morning I returned to this problem. After another false start I at last managed to get it. (-5,-5) is the ordered pair that fits the situation. The more of these problems I work through the easier it gets but still and fairly often I make these small mistakes that blow the game completely. Thanks again to all who helped me peel the scales off my eyes.
Click to expand...

In order for this to be correct, I must have been right in my (unstated) guess that you typed the problem itself wrong, and it is really

6x=5(x+y+3)-x
3(x-y)+4y=5(y+1)

not

6x=5(x+y+3)-x
3(x-y)+4y=5(y+x)

Am I right?
 
Dr.Peterson said:
In order for this to be correct, I must have been right in my (unstated) guess that you typed the problem itself wrong, and it is really

6x=5(x+y+3)-x
3(x-y)+4y=5(y+1)

not

6x=5(x+y+3)-x
3(x-y)+4y=5(y+x)

Am I right?
Click to expand...

Yes, I got it wrong. An inch the wrong way is as good as a mile in this business. It really teaches you to walk the line.
 
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