Question

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?
a. 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.
b. they will have the same solution because the first equations of both the systems have the same graph.
c. 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.
d. 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.

Answer 1

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.

Answer 2

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.