Consider the following set of equations: x + 2y = 5 4x + 8y = 12 3x + 6y + 3z…
1998
Consider the following set of equations:
x + 2y = 5
4x + 8y = 12
3x + 6y + 3z = 15
This set _____.
- A.
has a unique solution
- B.
has no solutions
- C.
has finite number of solutions
- D.
has infinite number of solutions
Attempted by 4 students.
Show answer & explanation
Correct answer: B
Compare the first two equations. From x + 2y = 5, multiplying both sides by 4 gives 4x + 8y = 20. But the second equation requires 4x + 8y = 12. The same left-hand side cannot equal both 20 and 12, so the system is inconsistent. Therefore, the set of equations has no solutions.