Answer: The correct option is (A) (3, -3).
Step-by-step explanation: We are given to solve the following system of equations :
[tex]5x+2y=9~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\2x-3y=15~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
We will be using the method of ELIMINATION to solve the given system.
Multiplying equation (i) by 3 and equation (ii) by 2, we have
[tex]3(5x+2y)=3\times9\\\\\Rightarrow 15x+6y=27~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)[/tex]
and
[tex]2(2x-3y)=2\times15\\\\\Rightarrow 4x-6y=30~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iv)[/tex]
Adding equations (iii) and (iv), we get
[tex]15x+4x=27+30\\\\\Rightarrow 19x=57\\\\\Rightarrow x=\dfrac{57}{19}\\\\\Rightarrow x=3[/tex]
And from equation (i), we get
[tex]5\times3+2y=9\\\\\Rightarrow 15+2y=9\\\\\Rightarrow 2y=-6\\\\\Rightarrow y=-\dfrac{6}{2}\\\\\Rightarrow y=-3.[/tex]
Thus, the required solution is (x, y) = (3, -3).
Option (A) is CORRECT.
