Solution of Equation

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Solution of Equation of 3x²-5xy+2y²=3

4x-3y=14

Solve the following Equations

3x²-5xy+2y²=3

4x-3y=14

Solution

3x²-5xy+2y²=33………. i

4x-3y=14……………. ii

We solve by substitution method

Make x to be the subject of the formular using Equation (ii)

Substitute it in above equation (i) above

3 )-5( +2y²=33

Multiply both side by 4

42+9y-70-15y+8y²=165

8y²-6y-193=0

y= -4.55102 or 5.30102

value of x = 0.086735 or 7.47576 Respectively

References

Haavelmo, T. (1943). The statistical implications of a system of simultaneous equations. Econometrica, Journal of the Econometric Society, 1-12.

Broyden, C. G. (1965). A class of methods for solving nonlinear simultaneous equations. Mathematics of computation, 19(92), 577-593.

Zellner, A., & Theil, H. (1992). Three-stage least squares: simultaneous estimation of simultaneous equations. In Henri Theil’s Contributions to Economics and Econometrics (pp. 147-178). Springer, Dordrecht.

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