How to solve

3x+2y=4
2x-3y=7
By proporgation value of variable

see whether this gives you some ideas:

http://softwareengineering.stackexchange.com/questions/158315/what-does-value-propagation-mean

However, elimination might be more useful here. You can manipulate the equations so that this is easy.

3x+2y=4
2x-3y=7

9x+6y = 12
4x-6y = 14

13x = 26
x = 2
so y = -1

Propagation value of variable is a very useful iterative method for solving system of equations, especially if certain variables have constraints.

The given example is especially favourable example for the method because the coefficients are diagonal dominant.
We rewrite the equations as:
x=(4-2y)/3, and
y=-(7-2x)/3
Using an arbitrary initial value of (1,1), i.e. x0=1,y0=1, we get
a new set as
x1=(4-2)/3=2/3
y1=-(7-2)/3=-5/3
Repeating, we have the following sets:
n x y
1 2/3 -5/3
2 22/9 -17/9
3 70/27 -19/27
4 146/81 -49/81
5 422/243 -275/243

We see that the 5th iteration evaluates to (1.737, -1.132)
which approaches the corrected answer of (2,-1).

However, the amazing fact is that if we apply Aitken's acceleration to the 1st, 3rd and 5th sets of results, we get exactly (2,-1).
Aitken's acceleration is given by:
X=((xn*xn+2-xn+1²)/(xn+xn+2-2xn+1)
Same applies to y.

To solve the system of equations using the method of propagation of variables, follow these steps:

Step 1: Multiply both equations by constants in a way that one of the coefficients of either x or y will have the same absolute value but opposite sign.

Equation 1: 3x + 2y = 4
Equation 2: 2x - 3y = 7

To eliminate the coefficient of y, multiply Equation 1 by 3 and Equation 2 by 2:
Equation 1: 9x + 6y = 12
Equation 2: 4x - 6y = 14

Step 2: Add the two equations together to eliminate the variable y.
(9x + 6y) + (4x - 6y) = 12 + 14
9x + 4x + 6y - 6y = 26
13x = 26

Step 3: Solve for x by dividing both sides of the equation by 13.
13x/13 = 26/13
x = 2

Step 4: Substitute the value of x into one of the original equations to solve for y. Let's use Equation 1.
3(2) + 2y = 4
6 + 2y = 4
2y = 4 - 6
2y = -2
y = -1

So, the solution to the system of equations is x = 2 and y = -1.