Determine the system which is equivalent to the system:
3x+4y=12
x-2y=9
a)
3x+4y=12
3x-6y=27
b)
3x+4y=12
2x-4y=18
c)
10y=-15
5x=30
d)
Any of A,B or C
In b, the first equation is unchanged.
In b, the second equation is multiplied by 2, every term, so it is unchanged.
In c, the values of x and y are explicit.
Substitute these values in A and B and see if they work.
To determine the equivalent system, we need to manipulate the given equations until they can be rearranged to have the same coefficients for the variables. Let's go through each option and see if they match the original system:
a)
The first equation is the same as the original system, 3x+4y=12.
The second equation, 3x-6y=27, is not the same as x-2y=9. Therefore, option a) is not equivalent to the original system.
b)
The first equation is the same as the original system, 3x+4y=12.
The second equation, 2x-4y=18, is not the same as x-2y=9. Therefore, option b) is not equivalent to the original system.
c)
The first equation, 10y=-15, is not the same as 3x+4y=12. Therefore, option c) is not equivalent to the original system.
d)
This option states that any of options a), b), or c) is equivalent to the original system. However, as we determined in our analysis of options a), b), and c), none of them are equivalent to the original system. Therefore, we can conclude that option d) is not correct.
In summary, none of the given options is equivalent to the original system: 3x+4y=12 and x-2y=9.