solve by the elimination method

[jlneedshelp]

Okay, so I understand how the elimination process works, but my problem is the fractions and decimals. I don't even know where to start. The problem is
0.3x - 0.2y = 4
0.2x + 0.5y = -21/23

I know to get out of decimals I can multiply by 100, but in this case since the second equation has a fraction what should I do? I've been trying to figure this out for a while now. Thanks for your help!

 

[Deleted member 4993]

Okay, so I understand how the elimination process works, but my problem is the fractions and decimals. I don't even know where to start. The problem is
0.3x - 0.2y = 4
0.2x + 0.5y = -21/23

I know to get out of decimals I can multiply by 100, but in this case since the second equation has a fraction what should I do? I've been trying to figure this out for a while now. Thanks for your help!

If you are absolutely incapable of working with fractions - then multiply everything with 230.

 

[jlneedshelp]

Great I'm not sure what I'm doing wrong now. Here are my steps:

0.3x - 0.2y = 4 (100)
0.2x + 0.5y = -21/23 (230)

30x - 20y = 400 (11.5)
46x - 115y = -210 (2)

345x - 230y = 4600
92x + 230y = -420
437x = -4180
x = 9.6

Then I plugged this into the first equation:
0.3(9.6) + 0.5y = 4
2.88 + 0.5y = 4
0.5y = 4 - 2.88
y= 1.12/.5
y= 2.2
Can you tell me where I went wrong?

 

[lookagain]

Okay, so I understand how the elimination process works, but my problem is the fractions and decimals. I don't even know where to start. The problem is
0.3x - 0.2y = 4
0.2x + 0.5y = -21/23

jlneedshelp,

you shouldn't even be given systems of equations with fractions and decimals in it. The problem
maker should stick with integers and fractions, or integers and decimals. A student should be
made to practice how to solve one of the types I explained. Although the system of equations
you presented is mathematically correctly presented, it is awkward in form and method of
solution.

 

[Denis]

0.2x + 0.5y = -21/23 (230)

46x - 115y = -210 (2)

+115y ; be careful :shock:

 

[mmm4444bot]

I'm not sure what I'm doing wrong now.

Did you check your arithmetic? Also, please proofread your typing before posting using the button provided.


0.3x - 0.2y = 4 (100)
0.2x + 0.5y = -21/23 (230)

I understand your intent above, but it's better to show the multiplication on both sides.


46x - 115y = -210

The subtraction sign is a typographical error.


437x = -4180

The negation sign is a typographical error.


x = 9.6

You're setting yourself up for round-off error here. Carrying four digits of precision is generally adequate to avoid round-off error in subsequent calculations.


2.88 + 0.5y = 4

The term 0.5y is not correct. Check your arithmetic.


1.12

This value shows round-off error.

Thank you for showing your work. You will go places.

 

[mmm4444bot]

It seems to me that you understand basic principles.

Have confidence to check your work, recognize your mistakes, and proceed.

Here's the solution, for your confirmation: y = -5.6522 and x = 9.5652

Are you taking a math course on-line?

 

[lookagain]

Re:

0.3x - 0.2y = 4 (100)
0.2x + 0.5y = -21/23 (230)

I understand your intent above, but it's better to show the multiplication on both sides.

jlneedshelp,

actually, you \(\displaystyle must\) show each side being multiplied by their respective "compensating
multipliers," because what you show done to one side must be shown being done to another.
Or you might choose not to bother showing the multiplications on each side at all. Or you might
state what you are doing to each side for the next step, and then write the new equations from
that, for example.


\(\displaystyle 100(0.3x - 0.2y) = 100(4)\)

\(\displaystyle 230(0.2x + 0.5y) = 230(-21/23)\)
-----------------------------------------------



\(\displaystyle 30x \ -\ 20y \ = \ 400\)

\(\displaystyle 46x + 115y = -210\)
-----------------------------


If you decide to eliminate the y terms by adding these two equations, note that the
least common multiple of their coefficients is 460.


\(\displaystyle 23(30x - 20y) = 23(400)\)

\(\displaystyle 4(46x + 115y) = 4(-210)\)
-------------------------------------



\(\displaystyle 690x - 460y = \ 9200\)

\(\displaystyle 184x + 460y = -840\)
------------------------------
\(\displaystyle 874x \ \ \ \ \ \ \ \ \ = \ \ 8360\)



\(\displaystyle x = \frac{8360}{874}\)


\(\displaystyle x = \frac{220}{23} . . . . . .exact \ (in \ lowest \ terms)\)


\(\displaystyle or \ x = \ \bigg{9}\frac{13}{23} . . . . . .exact\)


Then you can substitute a convenient form of the x-value into one
of the equations to solve for y. And then the exact solution to the
system of equations will be:


\(\displaystyle \bigg(\frac{220}{23}, \ \frac{-130}{23} \bigg)\)