Question

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

Pleaseeeeee help

Answer 1

option C is the correct answer

Explanation:

System A: System B:

-x - 2y = 7 ........(1) -x - 2y = 7 .......(3)

5x - 6y = -3 ........(2) -16y= 32 ........(4)

Solution for system A: ( -3, -2)

For option A

Multiply the first equation by 3

3(- x - 2y) = 3(7) ⇒ - 3x - 6y = 21 ........... (5)

Add equation 2 and 5

5x - 6y = -3

- 3x - 6y = 21

2x -12y = 18 ⇒ 2( x - 6y ) = 2( 9 ) ⇒ x - 6y = 9

Option A is not equal to equation in system B so now we check option B.

For option B

Multiply the first equation by -5

-5(- x - 2y) = -5(7) ⇒ 5x + 10y = -35 ........... (6)

Add equation 2 and 6

5x - 6y = -3

5x + 10y = -35

10x + 4y = -38 ⇒ 2( 5x + 2y ) = 2(-19) ⇒ 5x + 2y = -19

Option B is not equal to equation in system B so now we check option C.

For option C

Multiply the first equation by 5

5(- x - 2y) = 5(7) ⇒ - 5x - 10y = 35 ........... (7)

Add equation 2 and 7

5x - 6y = -3

- 5x - 10y = 35

0 - 16y = 32 ⇒ -16y = 32

Option C is equal to equation in system b so now we check if the solution to system B is same as system A.

Solution to system B:

First, we find value of y from equation 4:

-16y = 32 ⇒ y =
`(32)/(-16)` ⇒ y = -2

Now, we put value of y in equation 3 to find value of x:

-x - 2y = 7 ⇒ -x - 2(-2) = 7 ⇒ -x + 4 = 7 ⇒ -x = 7 - 4 ⇒ -x = 3

multiply both sides by -1

-1 × (-x) = -1 × (3) ⇒ x = -3

Solution of system B = (-3, -2)

Solution of system B is the same as system A, so option C is correct.