Answer: The correct option is (A) (4, -3).
Step-by-step explanation: We are given to solve the following system of linear equations and choose the correct ordered pair :
[tex]7x+8y=4~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\3x+2y=6~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
Multiplying equation (ii) by 4, we have
[tex]4(3x+2y)=4\times 6\\\\\Rightarrow 12x+8y=24~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)[/tex]
Subtracting equation (i) from equation (iii), we get
[tex](12x+8y)-(7x+8y)=24-4\\\\\Rightarrow 12x-7x=20\\\\\Rightarrow x=\dfrac{20}{5}\\\\\Rightarrow x=4.[/tex]
From equation (ii), we get
[tex]3\times4+2y=6\\\\\Rightarrow 12+2y=6\\\\\Rightarrow 2y=6-12\\\\\Rightarrow 2y=-6\\\\\Rightarrow y=-\dfrac{6}{2}\\\\\Rightarrow y=-3.[/tex]
Thus, the required solution is x = 4, y = -3 and the correct ordered pair is (4, -3).
Option (A) is CORRECT.
