Simultaneous Linear Equations

Q. A two-digit number is 6 times the sum of its digits. The number formed by reversing the digits is 25 less than the original number. Formulate the situations in simultaneous linear equations.

1. $4x-5y=09y-9x+25=0$
2. $5x-4y=09y-9x+25=0$
3. $4x-5y=0y-x+25=0$

Q. A number is greater than twice the other number by 8. Also, 5 times the smaller number exceeds the greater by 12. Convert these relations into simultaneous equations.

1. $x-2y-8=0$
   And, $x-5y+12=0$
2. $x-2y+8=0$
   And, $x-5y-12=0$
3. $2x-y-8=0$
   And, $5x-y+12=0$
4. $x-2y-12=0$
   And, $x-5y+8=0$

Q. Check whether system of simultaneous equations $2x+y=4$ and $y=2x$ have unique solution or not?

1. Yes it has unique solution
2. No, it does not have unique solution

Q. For the system of two linear simultaneous equations, Choose the appropriate statement

1. They can be intersecting lines
2. They can be non-intersecting and parallel lines
3. They can be identical lines
4. All of the above.

Q. 7 years from now Sam's age will be 3 times his daughter's age, and 4 years ago, Sam was 5 times as old as his daughter. Find the simultaneous equations for this situation.

1. $x-3y=14x-5y=-16$
2. $x+3y=14x+5y=-16$
3. $x-5y=14x-3y=-16$
4. None of the above

Q. Consider set of linear equations :$Qx+18y=27$ and $9y=12x+72$, Where $Q$ is a constant and no ordered pair satisfies both the equation simultaneously. Then, What will be the value of $Q$?

1. $Q=20$
2. $Q=-24$
3. $Q=24$
4. $Q=30$