8. The system below has the solution of (1,3) where A, B, C, D, E, and F are all nonzero real numbers.

Ax+By=C, Dx+Ey=F
Which of the following systems would not have (1,3) as the solution?
A- Ax+By=C & (2A-D)x+(2B+E)y=C-2F
B- Ax+By=C & 7Dx+7Ey=7F
C- Ax+By=C & (A+D)x+(B+E)y=C+F
D=(A/2+D)x+(B/2+E)y=(C/2+F) & Dx+Ey=F
Two systems of equations are shown below.

System A System B
6x+y=2 2x−3y=−10
−x−y=−3
−x−y=−3

7. Which of the following statements is correct about the two systems of equations?
A- They will have the same solution because the first equation of both the systems have the same graph.
B- 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.
C- 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.
D- 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.
System A- 6x+y=2, -x-y=-3
System B- 2x-3y=-10, -x-y=-3

For 7. The answer is B.

And for 8. The answer is A

8. The system that would not have (1,3) as the solution is:

A- Ax+By=C & (2A-D)x+(2B+E)y=C-2F

In this system, the first equation is the same as the given system. However, the second equation is different and does not have the same coefficients as the given system. Therefore, the solution (1,3) would not satisfy the second equation in system A.

7. The correct statement about the two systems of equations is:

B- 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.

In System B, the first equation can be obtained by adding the first equation of System A to 4 times the second equation of System A. Since this operation preserves the solution, the two systems will have the same solution.

To determine which of the following systems would not have (1,3) as the solution, we can substitute the values x=1 and y=3 into each system and see if the equations hold true.

A- Ax+By=C & (2A-D)x+(2B+E)y=C-2F
Substituting x=1 and y=3:
A(1) + B(3) = C
(2A-D)(1) + (2B+E)(3) = C-2F
These equations are satisfied when x=1 and y=3, so system A could have (1,3) as the solution.

B- Ax+By=C & 7Dx+7Ey=7F
Substituting x=1 and y=3:
A(1) + B(3) = C
7D(1) + 7E(3) = 7F
These equations are satisfied when x=1 and y=3, so system B could have (1,3) as the solution.

C- Ax+By=C & (A+D)x+(B+E)y=C+F
Substituting x=1 and y=3:
A(1) + B(3) = C
(A+D)(1) + (B+E)(3) = C+F
These equations are satisfied when x=1 and y=3, so system C could have (1,3) as the solution.

D- (A/2+D)x+(B/2+E)y=(C/2+F) & Dx+Ey=F
Substituting x=1 and y=3:
(A/2+D)(1) + (B/2+E)(3) = (C/2+F)
D(1) + E(3) = F
These equations are satisfied when x=1 and y=3, so system D could have (1,3) as the solution.

Therefore, all of the given systems could have (1,3) as the solution.

Moving on to the second question,

System A- 6x+y=2, -x-y=-3
System B- 2x-3y=-10, -x-y=-3

To determine which statement about these systems is correct, we need to analyze the equations and their coefficients.

Comparing the first equation of System A (6x+y=2) with the first equation of System B (2x-3y=-10), we can see that the coefficients of x and y are different.

In System A, the coefficient of x is 6, while in System B, the coefficient of x is 2. This means that the value of x for System B will not be equal to the value of x for System A. Therefore, we can eliminate option C.

Also, the first equation of System B (2x-3y=-10) is not obtained by adding a multiple of the second equation of System A to the first equation of System A. Therefore, we can eliminate option B.

Looking at the coefficients of x in the first equations of both systems, we see that the coefficient of x in System B (2x-3y=-10) is indeed 4 less than the coefficient of x in System A (6x+y=2). So, option D is the correct statement.

Therefore, the correct answer is D- 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.