Question

Choose the correct option that explains what steps were followed to obtain the system of equations below

Answer 1

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:

$5x -6y = -3 \\ -5x -10y =35$

⇒ Sum : $-16y = 32$

Now if we replace the second equation in system A with this $-16y = 32$ , then we will get the system B.

Solution of system B:

$-x -2y =7 \\ \\ -16y= 32$

First we will take the second equation as there is only one variable 'y'. So, we will solve that equation for 'y'

$-16y= 32\\\\ \frac{-16y}{-16} = \frac{32}{-16} \\ \\ y= -2$

Now for solving 'x', we will plug y= -2 into the first equation

$-x-2y= 7\\ \\ -x -2(-2) = 7\\ \\ -x +4 = 7 \\ \\ -x+4 -4 = 7-4 \\ \\ -x =3\\ \\ \frac{-x}{-1}= \frac{3}{-1}\\ \\ x= -3$

So, the solution of system B is (-3, -2), that means the solution of both systems are same.

Answer 2

The correct answer 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.