Question

What is the solution to this system of linear equations? 12q + 3r = 15 –4q – 4r = –44 (–18, 29) (–2, 13) (8, –1) (15, –44)

Answer 1

Answer:

(-2,13)

I believe this is the answer.

Answer 2

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 :

$12q+3r=15~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\-4q-4r=-44~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

Multiplying equation (ii) by 3, we have

$3(-4q-4r)=-44\times3\\\\\Rightarrow -12q-12r=-132~~~~~~~~~~~~~~~~~~~~~~~~(iii)$

Adding equations (i) and (iii), we get

$(12q+3r)+(-12q-12r)=15+(-132)\\\\\Rightarrow 3r-12r=15-132\\\\\Rightarrow -9r=-117\\\\\Rightarrow r=\dfrac{-117}{-9}\\\\\Rightarrow r=13.$

From equation (ii), we get

$-4q-4\times13=-44\\\\\Rightarrow -4q-52=-44\\\\\Rightarrow -4q=-44+52\\\\\Rightarrow -4q=8\\\\\Rightarrow q=\dfrac{8}{-4}\\\\\Rightarrow q=-2.$

Thus, the required solution is (q, r) = (-2, 13).

Option (B) is CORRECT.