Question

Two systems of equations are shown below: System A System B 3x + 2y = 3 −x − 14y = 1 −2x − 8y = −1 −2x − 8y = −1 Which of the following statements is correct about the two systems of equations? The value of x for System B will be one−third of the value of x for System A because the coefficient of x in the first equation of System B is one third times the coefficient of x in the first equation of System A. The value of x for System A will be equal to the value of y for System B because the first equation of System B is obtained by adding −4 to the first equation of System A and the second equations are identical. They will have the same solution because they represent the same lines when plotted on the coordinate axes. They will have the same solution because the first equation of System B is obtained by adding the first equation of System A to 2 times the second equation of System A.

Answer 1

(D)

Explanation:

Two linear equations by system A is given as:

`3x+2y=3` (1)

`-2x-8y=-1` (2)

Multiply equation (1) with 2 and equation (2) with 3 and then adding, we get

`6x+4 y-6x-24y=6-3`

`-20y=3`

`y=(-3)/(20)`

Putting the value of y in equation (1), we get

`3x-(6)/(20)=3`

`3x=(66)/(20)`

`x=(11)/(10)`

Two linear equations by system B is given as:

`-x-14y=1` (3)

`-2x-8y=-1` (4)

Multiply equation (3) with -2 and adding equation (4), we get

`2x+28y-2x-8y=-2-1`

`20y=-3`

`y=(-3)/(20)`

Putting the value of y in equation (3),we get

`-x+(42)/(20)=1`

`x=(11)/(10)`

As Two system , that is system (A) and System (B) has same solution.

Thus, Option (D) is correct. The two system will have the same solution because the first equation of System B is obtained by adding the first equation of System A to 2 times the second equation of System A.

Answer 2

The two linear equations represented in system A as :

3 x + 2 y =3 -------(1)

- 2 x - 8 y = -1 ------(2)

(1) × 2 + (2) × 3 gives

⇒ 6 x + 4 y - 6 x - 24 y = 6 -3

⇒ - 20 y = 3

⇒ y =
`(-3)/(20)`

Putting the value of y in equation (1), we get

`3 x  - (6)/(20)=3\\\\ 3 x= (66)/(20) \\\\ x=(11)/(10)`

Two linear equation represented in system B is:

3. -x - 14 y =1

4. - 2 x - 8 y = -1

-2 ×Equation (3) + Equation (4)=

2 x +28 y- 2 x - 8 y= -2 -1

⇒ 20 y = -3

⇒y =
`(-3)/(20)`

Putting the value of y in equation (3),we get

`-x + (42)/(20)=1 \\\\ x=(22)/(20)=(11)/(10)`

As Two system , that is system (A) and System (B) has same solution.

By looking at all the options , i found that Option (D) is correct. The two system will have the same solution because the first equation of System B is obtained by adding the first equation of System A to 2 times the second equation of System A.