Let `a ,b , c` be the real numbers. The following system of equations in `x ,y ,a n dz` `(x^2)/(a^2)+(y^2)/(b^2)-(z^2)/(a^2)=1,(x^2)/(a^2)-(y^2)/(b^2)+(z^2)/(a^2)=1,-(x^2)/(a^2)+(y^2)/(b^2)+(z^2)/(a^2)=1` has a. no solution b. unique solution c. infinitely many solutions d. finitely many solutions

Explanation

Given system of equation is ,
`(x^2)/(a^2)+(y^2)/(b^2)-(z^2)/(a^2)=1`,
`(x^2)/(a^2)-(y^2)/(b^2)+(z^2)/(a^2)=1`,
`-(x^2)/(a^2)+(y^2)/(b^2)+(z^2)/(a^2)=1`
Let `X=(x^2)/a^2`
`Y=(y^2)/(b^2)`
`Z=(z^2)/(c^2)`
we get,


`X+Y−Z=1`


`X−Y+Z=1`


`−X+Y+Z=1`
determinant is given by,
`Delta=[(1,1,-1),(1,-1,1),(-1,1,1)]`
`Delta=1(−1−1)−1(1+1)−1(1−1)`
`Delta=−4ne0`
Therefore this system of equations has a unique solution.