A system of equations and its solution are given below.
System A --> 5x - y = -11
3x - 2y = -8
Solution (-2, 1)
To get system B below, the second equation in system A was replaced by the sum of that equation and the first equation in system A multiplied by -2.
System B --> 5x - y = -11
?
A.
The second equation in system B is 7x = 30. The solution to system B will not be the same as the solution to system A.
B.
The second equation in system B is 7x = 30. The solution to system B will be the same as the solution to system A.
C.
The second equation in system B is -7x = 14. The solution to system B will be the same as the solution to system A.
D.
The second equation in system B is -7x = 14. The solution to system B will not be the same as the solution to system A.
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To get System B, we multiply the first equation in System A by -2 and add it to the second equation in System A.
Doing the math, we have:
-2(5x - y) + (3x - 2y) = -2(-11) + (-8)
-10x + 2y + 3x - 2y = 22 - 8
-7x = 14
Therefore, the second equation in System B is -7x = 14.
Since the second equation in both System A and System B is the same, the solution to System B will also be the same as the solution to System A.
Therefore, the correct answer is:
C. The second equation in system B is -7x = 14. The solution to system B will be the same as the solution to system A.