Google ClassroomAnswer two questions about Systems A and B :System A{x+3y=−92x+y=4{3x+4y=−92x+y=41) How can we get System B from System A ?Choese 1 answer:(A) Replace one equation with the sum/difference of both equationsReplace 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 equation2) 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
Q. Google ClassroomAnswer two questions about Systems A and B :System A{x+3y=−92x+y=4{3x+4y=−92x+y=41) How can we get System B from System A ?Choese 1 answer:(A) Replace one equation with the sum/difference of both equationsReplace 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 equation2) 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
Given Systems: System A is given by:{x+3y=−92x+y=4System B is given by:{3x+4y=−92x+y=4To determine how System B can be derived from System A, we need to compare the equations of both systems.
Comparison of Equations: By comparing the second equation of both systems, we can see that they are identical:2x+y=4This means that the second equation has not been changed when going from System A to System B.
Second Equation Comparison: Now, let's compare the first equations of both systems:System A: x+3y=−9System B: 3x+4y=−9We can see that the coefficients of x and 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.
First Equation Comparison: Let's perform the operation to check if it gives us the first equation of System B:(x+3y)+(2x+y)=(−9)+43x+4y=−5This does not result in the first equation of System B, which is 3x+4y=−9. Therefore, System B cannot be obtained by simply adding the two equations of System A.
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