Equation is not evaluating any result

Question

eq1 := $y = -26.21231979*z+15.42332896+13.22411533*e^{-.6786000000*x}$

eq2 := $y = -25.98077423*z+14.81943362+13.53858145*e^{-.6569000000*x}$

Comparing both equations, eliminating $y$

$-26.21231979*z+15.42332896+13.22411533*e^{-.6786000000*x}$ = $-25.98077423*z+14.81943362+13.53858145*e^{-.6569000000*x}$

Putting $z$= $0.5044$

$-26.21231979*(0.5044)+15.42332896+13.22411533*e^{-.6786000000*x} $= $ -25.98077423*(0.5044)+14.81943362+13.53858145*e^{-.6569000000*x}$

I cannot find $x$ value? I tried it in Maple as well. But it doesn't evaluate the value of $x$. Any other solution?

Edit : My main task is to calculate value of $x$ by putting any value of $z$ This is just an example

Answer 1

Why do you believe that there is a value of x that satisfies you equations when z=0.5044?

eq1 := y=-26.21231979*z+15.42332896+13.22411533*exp(-0.6786*x):
eq2 := y=-25.98077423*z+14.81943362+13.53858145*exp(-0.6569*x):
q := rhs(eq1)-rhs(eq2);
plot3d( [0,q], x=-0.001..0.001, z=0.4..1.4,view=-1..1,color=[red,blue] );
plot3d( [0,q], x=-10..10, z=0.4..1.4,view=-1..1,color=[red,blue] );
Optimization:-Minimize(z,{q<=0,q>=0},x=-0.001..0.001, z=1.1..1.3);

The surfaces computed by the above plot3d calls do not seem to fall below (or touch) height 0.0 unless z is at least some value greater than 1. Something above z=1.2496 or so. Do you have a reason to believe otherwise?

Answer 2

In Maple, use the command fsolve. Remember to use exp(x) for $e^x$.

Answer 3

I suppose that the value you gave to "z" is wrong or that your coefficients are wrong. Using the numbers given in your post, there is no solution to your problem. In order to have a solution close to x=0.501, "z" should be of the order of 1.18421 (as reported by acer). The difference of your two equations goes to an extemum for x = 0.414684 and for this value this difference has a value equal to (-0.274199 + 0.231546 z).