Solve the system of equations by​ elimination, if a solution exists.

Question

12 x
minus
3 y
equals
8
6 x
minus
1.5 y
equals
negative 16
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Part 1
Select the correct answer below​ and, if​ necessary, fill in any answer boxes to complete your choice.
A.
The solution of the system is xequals
  
enter your response here and yequals
  
enter your response here. ​(Type integers or simplified​ fractions.)
B.
There are infinitely many solutions.
C.
There is no solution.

Answer 1

To solve the given system of equations by elimination, we first rewrite the equations for clarity:

1. \( 12x - 3y = 8 \) (Equation 1)
2. \( 6x - 1.5y = -16 \) (Equation 2)

We can eliminate the decimals in Equation 2 by multiplying the entire equation by 2:

\[ 2(6x - 1.5y) = 2(-16) \] This gives us: \[ 12x - 3y = -32 \quad (Equation 3) \]

Now, we have the following two equations:

1. \( 12x - 3y = 8 \) (Equation 1)
2. \( 12x - 3y = -32 \) (Equation 3)

Next, we notice that both equations 1 and 3 have the same left-hand side \( (12x - 3y) \). This gives us:

\[ 8 = -32 \]

This statement is clearly false.

Since the system leads to a contradiction, it implies that there is no solution to the system of equations.

Thus, the correct answer is: C. There is no solution.