The correct option will be :
A. To get system B, the second equation in system A was replaced by the sum of that equation and the first equation multiplied by 5. The solution to system B will be the same as the solution to system A.
System A :
-x - 2y = 7 ..........(1)
5x - 6y = -3 ..........(2)
If we multiply the first equation by 5, then we will get :
5(- x - 2y) = 5(7)
⇒ - 5x - 10y = 35 ........... (3)
Now the Sum of equation (2) and equation (3) is:
[tex] 5x -6y = -3 \\ -5x -10y =35 [/tex]
⇒ Sum : [tex] -16y = 32 [/tex]
Now if we replace the second equation in system A with this [tex] -16y = 32 [/tex] , then we will get the system B.
Solution of system B:
[tex] -x -2y =7 \\ \\ -16y= 32 [/tex]
First we will take the second equation as there is only one variable 'y'. So, we will solve that equation for 'y'
[tex] -16y= 32\\\\ \frac{-16y}{-16} = \frac{32}{-16} \\ \\ y= -2 [/tex]
Now for solving 'x', we will plug y= -2 into the first equation
[tex] -x-2y= 7\\ \\ -x -2(-2) = 7\\ \\ -x +4 = 7 \\ \\ -x+4 -4 = 7-4 \\ \\ -x =3\\ \\ \frac{-x}{-1}= \frac{3}{-1}\\ \\ x= -3 [/tex]
So, the solution of system B is (-3, -2), that means the solution of both systems are same.
