solve two equations for two unknown variables

how can i solve two equations for two unknown variables?

like these two:

z=f1(x)+f2(y)
z=f3(x)+f4(y)

for z=0

please help, thx in advance.

Answer 1

[Dr. Seis]

G*m = d

G = [f1,f2;f3,f4];
d = [z1;z2];
m = G\d;
x = m(1);
y = m(2);

Answer 2

[Walter Roberson]

That cannot be solved without knowing f1(x), f2(y), f3(x), f4(y)

Are f1, f2, f3, and f4 perhaps constants, as in f1*x + f2*y ? If so then the solution is x = 0, y = 0, unless f1*f4 = f2*f3

[yasser]

yes, f1,f2,f3&f4 are constants.

Answer 3

[yasser]

now how can i solv it?

[Walter Roberson]

If your equations are

0=f1*x+f2*y

0=f3*x+f4*y

then the only solution is x = 0 and y = 0, unless it happens that f1*f4 = f2*f3 is exactly zero.

If f1*x + f2*y = 0 then y = -f1/f2 * x . Substitute this in to f3*x + f4*y = 0, and you end up with -x*(f1*f4-f3*f2)/f2 = 0 . That has solutions only if x = 0 or f1*f4-f3*f2 = 0 . If you try x = 0 then because f1*x + f2*y = 0, then f1 * 0 + f2*y = 0, then f2 * y = 0, which has a solution only if y = 0 or f2 = 0. But if f2 = 0 then the solution for x would have had a division by 0 so that possibility is out. This leaves only x = 0 and y = 0, or f1*f4 = f2*f3

Answer 4

[Brian]

you can solve a 2x2 by substitution or you can use rref.m. substitution is probably easier in this case!

Answer 5

[yasser]

sorry, my bad in my case , i would say z1=ax+by z2=cx+dy a,b,c,d constants i want to put z1=const1 & z2=const2 then solve and find x & y ?

[Walter Roberson]

x = (f4*z1-f2*z2)/(f1*f4-f3*f2)

y = (f1*z2-f3*z1)/(f1*f4-f3*f2)

Answer 6

[yasser]

@elige grant thx alot