mistgirl
contestada

Two systems of equations are shown:

System A System B

6x + y = 2 2x − 3y = −10

−x − y = −3 −x − y = −3


Which of the following statements is correct about the two systems of equations?


The value of x for System B will be 4 less than the value of x for System A because the coefficient of x in the first equation of System B is 4 less than the coefficient of x in the first equation of System A.


They will have the same solution because the first equations of both the systems have the same graph.


They will have the same solution because the first equation of System B is obtained by adding the first equation of System A to 4 times the second 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.

Respuesta :

The correct statement is that 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. Option D

How to determine the right statement

6x + y = 2 2x − 3y = −10    System A

-x − y = −3 −x − y = −3 System B

Let;s solve for x and y in system A

6x + y = 2

Make 'y' the subject

y = 2-6x

Substitute in the other equation

-x -y = -3

-x - (2-6x) = -3

-x -2+6x = -3

Collect like terms

5x = -3+2

x = -1/5

Substitute in y = 2-6x to find 'y'

y = 2- 6(-1/5)

y = 2+ 6/5

y = [tex]\frac{10+ 6}{5}[/tex]

y = 16/5

For system B

-x-y = -3

Make y subject, we have

-x + 3 = y

y = -x + 3

Substitute in the other equation, we have

2x − 3y = −10

2x - 3(-x+3) = -10

2x + 3x -9 = -10

Collect like terms

5x -9 = -10

5x = -10 + 9

x = 1/5

Substitute into y = -x + 3 to find 'y'

y = -(1) + 3

y = 2

Thus, the correct statement is that 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. Option D

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