How do you solve a equation with three variables?

Answer 1

To solve any system of equations the no. of equations must be the same as are the number of variables.

To define the case in words, choose any two equations from the set of three and eliminate one of the variables. now among the three equations select another different pair(obviously one of the equation in the new pair would be same as in the last pair). now again eliminate the same variable by substitution method from here towo equations in two variables will resolve in values of two variables. third variable can be resolved simultaneously using any of three equations..

example..

3x + 4y + 2z = 17 eq1; x + 3y + 2z = 13 eq2; 2x + 2y + z = 9 eq3

solution..using eq1 and eq2; x + 3y + 17 - 3x - 4y = 13

we have -2x -y + 4 = 0 eq4

using equation 2 and equation 3;

x + 3y + 2(9 - 2x - 2y) = 13 eq5

we have -3x -y + 5 =0

soving eq4 and eq5

x=1 and y=2

substituting x and y in eq1 we have

3(1) + 4(2) + 2z = 17 that is we have z = 3

so x = 1, y=2 and z=3

i hope it was useful.kindly comment...............