Answer: the correct option is (C) (2, 5).
Step-by-step explanation: We are given to use the substitution method to solve the following system of equations :
[tex]2y+4x=18~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\2y-3x=4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
Dividing equation equation (i) on both sides by 2, we have
[tex]\dfrac{2y+4x}{2}=\dfrac{18}{2}\\\\\Rightarrow y+2x=9\\\\\Rightarrow y=9-2x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)[/tex]
Substituting the value of y from equation (iii) in equation (ii), we get
[tex]2(9-2x)-3x=4\\\\\Rightarrow 18-4x-3x=4\\\\\Rightarrow 18-4=4x+3x\\\\\Rightarrow 14=7x\\\\\Rightarrow x=\dfrac{14}{7}\\\\\Rightarrow x=2.[/tex]
So, from equation (iii), we get
[tex]y=9-2\times2=9-4=5.[/tex]
Thus, the required solution of the given system is (x, y) = (2, 5).
Option (C) is CORRECT.
