- Thread starter Sambo
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A valid but, non-traditional method: isDoes anyone know the ordered pair that is solution to:

3x-2y=5 and 5x+3y=4

1--3x-2y = 10

2--Dividing by the lowest coefficient yields x + x/2 + y = 5

3--x/2 must be an integer k making x = 2k.

4--Substituting back into (1) yields 6k - 2y = 10 making y = 3x - 5

5--k....0....1....2....3

...x....0....2....4....6

...y...-5...-2...+1....4

6--5x + 3y = 4

7--Dividing through by 3 yields x + 2x/3 + y = 1 + 1/3

8--(2x - 1)/3 must be an integer

9--Wanting the coefficient of x to be 1, (4x - 2)/3 must also be an integer.

10--Dividing by 3 yields x + x/3 - 2/3

11--((x - 2)/3 is an integer k making x == 3k + 2

12--k....0....1....2....3

....x....2....5....8...11

....y...-2...-7..-12..-17

By inspection, (2,-2) is the common ordered pair solution for these two equations.

You can and SHOULD check your solution yourself. If you believe the solution is (2, -2), then substitute 2 for x and -2 for y in each of the two equations. If both equations are true, you know the solution is correct.Sambo said:Does anyone know the ordered pair that is solution to: 3x-2y=10

5x+3y=4

I get 2,-2

If one of the equations is NOT true, you know you have made an error.