Respuesta :
Answer:
Step-by-step explanation:
To determine the number of solutions for this system of equations, we can use the concept of linear independence.
The given system of equations can be written in matrix form as:
| 1 2 | | x | | 3 |
| 4 8 | * | y | = | 15 |
If we calculate the determinant of the coefficient matrix, which is the matrix on the left side of the equation, we can determine whether the system has a unique solution, infinitely many solutions, or no solution.
Calculating the determinant of the coefficient matrix:
| 1 2 |
| 4 8 |
Determinant = (1 * 8) - (2 * 4) = 8 - 8 = 0
Since the determinant is equal to zero, the system of equations has infinitely many solutions.
Therefore, the given system of equations has infinitely many solutions.
