Unique solution of Poseidon Vault puzzle #shorts

Is the pair of linear equations 2x+y=5 and 3x+2y=8 has unique solution ? In case there is a unique solution,find it by using cross multiplication method.

The equation |x+1|^(log)_(("x"+1))(3+2-x^(2))=(x-3)|x| has a. unique solution b. two solutions c. no solution d. more than two solution

In a crossword puzzle 10 words are to be guessed of which 5 words have each an alternative solution also.No.of possible solutions is

If am= bl, then find whether the pair of linear equations ax + by= c and lx + my = n has no solution, unique solution or infinitely many solutions

If ad!=bc then find whether the pairs of linear equations ax+by=p and cx+dy=q has no solution,unique solution or infinitely many solutions

The system of linear equations x+y+z=2;2x+3y+2z=5,2x+3y+(a^(2)-1)z=6 has unique solution if |a|!=sqrt(3) is inconsistent if |a|=sqrt(3) has unique solution if |a|=sqrt(3) has infinite solutions if |a|=sqrt(3)

If am!=bl, then the system of equations ax+by=c,quad lx+my=n( a) has a unique solution (b) has no solution ( c) has infinitely many solutions (d) may or may not have a solution

Find the values of k for which the system 2x+ky=13x-5y=7 will have ( i ) a unique solution,and (ii) no solution.Is there is a value of k for which the solution.Is there is many solutions?

a irax by c and lix my n has unique solutions then find the relation between the coefficients

Consistency (unique/infinite solutions) and inconsistent (no solution) system