Web Analytics
Answered

Two systems of equations are shown below: 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?

Athe 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
Bthey will have the same solution because the first equations of both the systems have the same graph.
Cthey 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
Dthe 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.

Verified Answer :

Answer:

option (C) is correct.

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.

Step-by-step explanation:

Given two system of  equations

System A :  6x + y = 2  , -x -y = -3

System B :  2x - 3y = -10  , -x -y = -3

We have to choose out of given statements that is true about the the two systems of equations.

Consider system A:

6x + y = 2   ......(1)

-x -y = -3      ....(2)

Multiply equation (2) by 4, we get,

-4x -4y = -12  ......(3)

Now adding, (1) and (3) , we have,

6x + y +(-4x - 4y) = 2 - 12

Solving, we get,

6x + y -4x - 4y = 2 - 12

2x - 3y = - 10   which is equation (1) of system B.

We now find the solution to the system A.

adding equation  (2) and (1) ,we have,

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

6x + y - x -y = 2 -3

5x = -1

\(x=\frac{-1}{5}\)

Put value of x in (2) , we get, \(y=\frac{16}{5}\)

We now find the solution to the system B.

System B :  2x - 3y = -10  ........(4)

-x -y = -3 .....(5)

Multiply equation (5) by 3 , we have

-3x -3y = -9 .......(6)

Subtract equation  (6) from (4) ,we have,

2x - 3y-(-3x - 3y) = -10 +9

5x = -1

\(x=\frac{-1}{5}\)

Put value of x in (5) , we get, \(y=\frac{16}{5}\)

Thus, both system A and B have same value.

Thus, option (C) is correct.

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.

ShaniahPoweska

Answer:

yhe answer is C

Step-by-step explanation:

I took the test

Related Questions