Answer: The correct option is (b) (6, 4).
Step-by-step explanation: We are given to use the substitution method to solve the following system of equations :
[tex]13x-2y=70~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\2x-2y=4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
From equation (ii), we have
[tex]2x-2y=4\\\\\Rightarrow x-y=2\\\\\Rightarrow x=y+2~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)[/tex]
Substituting the value of x from equation (iii) in equation (ii), we get
[tex]13x-2y=70\\\\\Rightarrow 13(y+2)-2y=70\\\\\Rightarrow 13y+26-2y=70\\\\\Rightarrow 11y=70-26\\\\\Rightarrow 11y=44\\\\\Rightarrow y=\dfrac{44}{11}\\\\\Rightarrow y=4.[/tex]
From equation (iii), we get
[tex]x=y+2=4+2=6.[/tex]
Thus, the correct ordered pair solution of the given system is (x, y) = (6, 4).
Option (b) is CORRECT.
