Question

What is the solution (a, c) to this system of linear equations?

Answer 1

Answer:  The correct option is

(C) (3, 4).

Step-by-step explanation:  We are given to find the solution (a, c) to the following system of linear equations :

$2a-3c=-6~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\a+2c=11~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

Multiplying equation (ii) by 2, we have

$2(a+2c)=2\times11\\\\\Rightarrow 2a+4c=22~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)$

Subtracting equation (i) from (iii), we get

$(2a+4c)-(2a-3c)=22-(-6)\\\\\Rightarrow 7c=28\\\\\Rightarrow c=\dfrac{28}{7}\\\\\Rightarrow c=4.$

From equation (i), we get

$2a-3\times4=-6\\\\\Rightarrow 2a=12-6\\\\\Rightarrow 2a=6\\\\\Rightarrow a=\dfrac{6}{2}\\\\\Rightarrow a=3.$

Thus, the required solution is (a, c) = (3, 4).

Option (C) is CORRECT.

Answer 2

This is how you do it :) let me know if you have any questions. Hope this helps :)