Hello,
I am familiar with using matrices to solve for multivariables with many equations.
For example, if we have:
x + 2z -y = 1
z + y= 2
It can be entered as...
1 2 -1 1
0 -1 1 -2
BUT what is the equation is more complex such as
x + yz + (1/(yz)).... something that has variables being multiplied or divided together?
Thanks in advance! Bizzy
You can do it the way you first learned how to solve linear equations in multiple unknowns back in eighth grade.
[1] f(x, y, z) = a.
[2] g(x, y, z) = b.
[3] h(x, y, z) = c.
Solve equation 1 for x in terms of y, z, and a to get
[4] x = j(a, y, z).
Substitute j(a, y, z) for x in equations 2 and 3 to get:
[2a] k(a, y, z) = b. Note that a is a constant, a known number.
[3a] m(a, y, z) = c.
Solve equation 2a for y in terms of a, b, and z to get:
[5] y = n(a, b, z). Note that a and b are constants, known numbers.
Substitute n(a, b, z) for y in equation 3a to get:
[3b] p(a, b, z) = c.
Solve equation 3b for z in terms of a, b, and c to get
[6] z = q(a, b, c). Note that a, b, and c are constants, known numbers. So this equation can (presumably) be solved.
Because the initial equations are not linear, there may be multiple solutions for z.
Put each solution for z into equation 5 and solve for y. Again there may be multiple solutions for y for each solution of z.
Put each combination of solutions for y and z into equation 4 and solve for x. Again there may be multiple solutions for x for each combination of y and z.
