Answer: Option (A) (0, 2) is the correct.
Step-by-step explanation: We are given to select the correct ordered pair that is a solution to the following system of linear equations :
\(2x+3y=6~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\-3x+5y=10~~~~~~~~~~~~~~~~~~~~~~~~~(ii)\)
Multiplying equations (i) and (ii) by 3 and 2 respectively, we have
\(6x+9y=18~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)\\\\-6x+10y=20~~~~~~~~~~~~~~~~~~~~~~~~(iv)\)
Adding equations (iii) and (iv), we get
\(9y+10y=18+20\\\\\Rightarrow 19y=38\\\\\Rightarrow y=\dfrac{38}{19}\\\\\Rightarrow y=2.\)
Substituting the value of y in equation (ii), we get
\(-3x+5\times2=10\\\\\Rightarrow -3x+10=10\\\\\Rightarrow -3x=0\\\\\Rightarrow x=0.\)
Thus, the required ordered pair solution is (0, 2).
Option (A) is CORRECT.
