Question

Two systems of equations are shown below:

System A
6x + y = 2
2x − 3y = −10
System B
−x − y = −3
−x − y = −3
Which of the following statements is correct about the two systems of equations? (5 points)

Group of answer choices

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.

Answer 1

The solution of the equations in system A is,

(x,y) = (-0.8 , 2.8)

The system of equation B contains 2 identical equations or only 1 equation which will be represented by a straight line and will have infinite no. of solutions.

Explanation:

The equations in system A are,

6x + y = -2 -----------------(1)

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

Doing
`(1) * 3 + (2)` we get,

20x = -16

⇒ x = - 0.8 --------------------(3)

From (3) putting the value of x in (1) we get,

y =
`(-6) * (-0.8) -2`

= 2.8 -----------------------(4)

So the solution is, (x , y) = (-0.8 , 2.8)

The system of equation B contains 2 identical equations or only 1 equation which will be represented by a straight line and will have infinite no. of solutions.