Question

Determine the number of solutions for this system of equations by inspection only. Explain.
5xplus2y
equals
16
30 x plus 12 y
equals
118
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Part 1
Select the correct answer below and fill in the answer box to complete your choice.
A.
There is one solution. If the first equation is multiplied by
  
enter your response here​, the​ x-terms will be the same but the​ y-terms will not.​ So, the​ x-term will be eliminated leaving a​ y-term and a constant.
B.
There are infinitely many solutions. If the first equation is multiplied by
  
enter your response here​, the like variable terms and constants will be the same.​ So, each term will be eliminated. This results in the statement 0equals​0, which is true.
C.
There is no solution. If the first equation is multiplied by
  
enter your response here​, the like variable terms will have the same​ coefficients, but the constants will not be the same.​ So, the variable terms will be​ eliminated, but the constant term will not be zero. This results in a statement that is not true.

Answer 1

C. There is no solution. If the first equation is multiplied by 6, the like variable terms will have the same coefficients, but the constants will not be the same.

5x + 2y = 16 → multiply by 6 → 30x + 12y = 96, which contradicts 30x + 12y = 118, yielding 0 = 22. Thus no solution.