# solution to system of equations: 3x-2y=10, 5x+3y=4

#### Sambo

##### New member
Does anyone know the ordered pair that is solution to:

3x-2y=10
5x+3y=4

I get 2,-2

You are correct.

#### TchrWill

##### Full Member
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.

#### Mrspi

##### Senior Member
Re: solution to system of equations

Sambo said:
Does anyone know the ordered pair that is solution to: 3x-2y=10
5x+3y=4

I get 2,-2
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.

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