Re: solution to system of equations
Does anyone know the ordered pair that is solution to:
3x-2y=5 and 5x+3y=4
A valid but, non-traditional method: is
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.