Respuesta :
Answer: The correct option is (B) (-2, 13).
Step-by-step explanation: We are given to find the solution of the following system of equations :
[tex]12q+3r=15~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\-4q-4r=-44~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
Multiplying equation (ii) by 3, we have
[tex]3(-4q-4r)=-44\times3\\\\\Rightarrow -12q-12r=-132~~~~~~~~~~~~~~~~~~~~~~~~(iii)[/tex]
Adding equations (i) and (iii), we get
[tex](12q+3r)+(-12q-12r)=15+(-132)\\\\\Rightarrow 3r-12r=15-132\\\\\Rightarrow -9r=-117\\\\\Rightarrow r=\dfrac{-117}{-9}\\\\\Rightarrow r=13.[/tex]
From equation (ii), we get
[tex]-4q-4\times13=-44\\\\\Rightarrow -4q-52=-44\\\\\Rightarrow -4q=-44+52\\\\\Rightarrow -4q=8\\\\\Rightarrow q=\dfrac{8}{-4}\\\\\Rightarrow q=-2.[/tex]
Thus, the required solution is (q, r) = (-2, 13).
Option (B) is CORRECT.
