Answer: The correct option is (B) (4, 9).
Step-by-step explanation: We are given to use the elimination method to solve the following system of equations :
[tex]x-3y=-23~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\5x+6y=74~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
Multiplying equation (i) by 2, we have
[tex]2(x-3y)=2\times (-23)\\\\\Rightarrow 2x-6y=-46~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)[/tex]
Adding equations (ii) and (iii), we get
[tex](5x+6y)+(2x-6y)=74-46\\\\\Rightarrow 7x=28\\\\\Rightarrow x=\dfrac{28}{7}\\\\\Rightarrow x=4.[/tex]
From equation (i), we again get
[tex]x-3y=-23\\\\\Rightarrow 4-3y=-23\\\\\Rightarrow 3y=4+23\\\\\Rightarrow 3y=27\\\\\Rightarrow y=\dfrac{27}{3}\\\\\Rightarrow y=9.[/tex]
Thus, the required solution of the given system is (x, y) = (4, 9).
Option (B) is CORRECT.
