somebody please help...
I stuck with these 2 problems for a long time not sure that it is defined or not
Question 1: Give all solutions, if any, of
x + y =1
sin(x - y) =1/2
with 0 less than or equal to X and X is less than or equal to 3
Question 2: Give all solutions, if any, of
sinx +siny = -1
sinx - siny + 4cosz =1
sinx + siny + 2cosz =2
For this problem; after I did Gauss Ellimination, I got
[1 1 0 -1]
[0 1 -2 -1]
[0 0 1 3/2] Then z=3/2, y=2, x=-3
but siny=sin2=undefined and sinx=sin(-3)=undefined
I am not sure what I have done wrong, please help
In Question 2, I believe you found the supposed values of sin(x), sin(y) and cos(z) correctly. Since sin(x) = -3 has no solutions, the original systems has no solutions, either.
For Question 1, express y through x from the first equation, substitute it into the second equation and use the fact that iff , or , . Select suitable values of x between 0 and 3.
The second problem has no real solutions.
Question 2: Give all solutions, if any, of: .
Substitute  into : .
. . Hence: . . . . no real roots.
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
By the way, Gaussian elimination could be used
. . with an appropriate substitution.
Then we have: .
Gaussian elimination results in: .
And we have: .
. . None of the equations has a real solution.