Help to solve Simultaneous Equations

Question

I think this should be easy to numerically solve in Mathematica, but for some reason I'm not finding the correct way to do it.

I basically want to solve these simyltaneous equiations:

NSolve[
{
-(0.7)*w + (0.3)*y + (0.4)*z == 0,
-(0.6)*x + (0.2)*y + (0.1)*z == 0,
(0.5)*w + (0.3)*x - y == 0,
(0.2)*w + (0.3)*x + (0.5)*y - (0.5)*z == 0,                                \
w + x + y + z == 1
}, 
{z , w , x , y}]

This is what i see:

Answer 1

Try this:

Clear[x, y, z, w];
eq1 = -0.7*w + 0.3*y + 0.4*z == 0;
eq2 = -0.6*x + 0.2*y + 0.1*z == 0;
eq3 = 0.5*w + 0.3*x - y == 0;
eq4 = 0.2*w + 0.3*x + 0.5*y - 0.5*z == 0;
eq5 = w + x + y + z == 1;
Solve[{eq1, eq2, eq3, eq4, eq5}, {z, w, x, y}]

The result is

{{z -> 0.384513, w -> 0.300401, x -> 0.126836, y -> 0.188251}}

I removed unnecessary parentheses. It seems that they were misleading for Mathematica.

The solution of 5 equation with 4 variables is possible, since the determinant of first 4 equations is zero:

  m = {{-0.7, 0, 0.3, 0.4}, {0, -0.6, 0.2, 0.1}, {0.5, 0.3, -1, 
    0}, {0.2, 0.3, 0.5, -0.5}, {1, 1, 1, 1}};
m[[1 ;; 4]] // Det // Chop

0

You could have skip one of them.