Chinese Method of solving equations?

Question

Can anyone explain to me how to solve the equations 2x+4y=6 and 4x-3y=-10 simultaneously???
Using the Chinese method that is.
x

Answer 1

Write the equations as a matrix, leaving out the variables:

________
2 | 4 | 6 |
-------------
4 |-3 | -10 |
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The next step should aim to get a zero into one of the elements of the matrix. We can do this by first multiplying the top row by 2

________
4 | 8 | 12 |
-------------
4 |-3 | -10 |
--------------

Now we subtract the first row from the second:

________
4 | 8 | 12 |
-------------
0 | -11 | -22 |
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The second row shows that y = -22 / -11 = 2.

To get a zero into the top row, we can first multiply it by 11:

___________
44 | 88 | 132 |
------------------
0 | -11 | -22 |
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Now add the second row to the first 8 times:

___________
44 | 0 | -44 |
------------------
0 | -11 | -22 |
-------------------

x is thus -44 / 44 = -1.

Check:

2 * (-1) + 4 * 2 = 6

Yes!!!

4 * (-1) - 3 * 2 = -10

Yes!!!

Answer 2

I am not sure what exactly is the Chinese method, but the way i would solve this equation is as follows:
2x+4y=6
Then x= 3-2y
substitute this into the second equation:
4x-3y=-10
4(3-2y) -3y=-10
12-8y-3y=-10
22=11y
2=y
Now substitute to find x:
x=3-2y=3-4=-1

x=-1, y=2

Answer 3

It is similar to matrix algebra. You woul set up 2 colums containing the coefficients of each equation so it would look like this;

2 4
4 -3
6 -10

Now you manipulate the columns until the two fours become zeroes and the last two digits in each row become the solution.
They work with columns, we work with rows.

Answer 4

I've never heard of the Chinese method... and I'm Chinese.
BTW, y=2 and x=-1

Answer 5

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