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Google Classroom
Answer two questions about Systems 
A and 
B :
System 
A

{[x+3y=-9],[2x+y=4]quad{[3x+4y=-9],[2x+y=4]:}

How can we get System 
B from System 
A ?

Choese 1 answer:
(A) Replace one equation with the sum/difference of both equations
Replace only the left-hand side of one equation with the sum/difference of the left-hand sides of both equations
(C) Replace one equation with a multiple of itself
(D) Replace one equation with a multiple of the other equation
2) Based on the previous answer, are the systems equivalent? In other words, do they have the same solution?
Choese 1 answer:
(A) Yes
(D) No

Google Classroom\newlineAnswer two questions about Systems A A and B B :\newlineSystem A A \newline{x+3y=92x+y=4{3x+4y=92x+y=4 \left\{\begin{array}{l}x+3 y=-9 \\ 2 x+y=4\end{array} \quad\left\{\begin{array}{l}3 x+4 y=-9 \\ 2 x+y=4\end{array}\right.\right. \newline11) How can we get System B B from System A A ?\newlineChoese 11 answer:\newline(A) Replace one equation with the sum/difference of both equations\newlineReplace only the left-hand side of one equation with the sum/difference of the left-hand sides of both equations\newline(C) Replace one equation with a multiple of itself\newline(D) Replace one equation with a multiple of the other equation\newline22) Based on the previous answer, are the systems equivalent? In other words, do they have the same solution?\newlineChoese 11 answer:\newline(A) Yes\newline(D) No

Full solution

Q. Google Classroom\newlineAnswer two questions about Systems A A and B B :\newlineSystem A A \newline{x+3y=92x+y=4{3x+4y=92x+y=4 \left\{\begin{array}{l}x+3 y=-9 \\ 2 x+y=4\end{array} \quad\left\{\begin{array}{l}3 x+4 y=-9 \\ 2 x+y=4\end{array}\right.\right. \newline11) How can we get System B B from System A A ?\newlineChoese 11 answer:\newline(A) Replace one equation with the sum/difference of both equations\newlineReplace only the left-hand side of one equation with the sum/difference of the left-hand sides of both equations\newline(C) Replace one equation with a multiple of itself\newline(D) Replace one equation with a multiple of the other equation\newline22) Based on the previous answer, are the systems equivalent? In other words, do they have the same solution?\newlineChoese 11 answer:\newline(A) Yes\newline(D) No
  1. Given Systems: System A is given by:\newline{x+3y=92x+y=4 \begin{cases} x + 3y = -9 \\ 2x + y = 4 \end{cases} \newlineSystem B is given by:\newline{3x+4y=92x+y=4 \begin{cases} 3x + 4y = -9 \\ 2x + y = 4 \end{cases} \newlineTo determine how System B can be derived from System A, we need to compare the equations of both systems.
  2. Comparison of Equations: By comparing the second equation of both systems, we can see that they are identical:\newline2x+y=4 2x + y = 4 \newlineThis means that the second equation has not been changed when going from System A to System B.
  3. Second Equation Comparison: Now, let's compare the first equations of both systems:\newlineSystem A: x+3y=9 x + 3y = -9 \newlineSystem B: 3x+4y=9 3x + 4y = -9 \newlineWe can see that the coefficients of x x and y y in the first equation of System B are both one more than their respective coefficients in the first equation of System A. This suggests that the first equation of System B could be derived by adding the second equation of System A to the first equation of System A.
  4. First Equation Comparison: Let's perform the operation to check if it gives us the first equation of System B:\newline(x+3y)+(2x+y)=(9)+4 (x + 3y) + (2x + y) = (-9) + 4 \newline3x+4y=5 3x + 4y = -5 \newlineThis does not result in the first equation of System B, which is 3x+4y=9 3x + 4y = -9 . Therefore, System B cannot be obtained by simply adding the two equations of System A.

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