The given system of equations is:
2x + 3y = 1
-3x - 2y = -1
To find the number of solutions, we can use the concept of determinants. If the determinant of the coefficient matrix is non-zero, the system has one unique solution. If the determinant is zero, the system can either have infinitely many solutions or no solutions.
The determinant of the coefficient matrix is:
| 2 3 |
| -3 -2 |
= (2 * -2) - (3 * -3)
= 4 + 9
= 13
Since the determinant is non-zero (i.e., 13 is not zero), the system has one unique solution.
Therefore, the correct answer is: one solution.
How many solutions does the following system have?
2x+3y=1
-3x-2y=-1
%0D%0A%0D%0A %0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0Ainfinitely many solutions%0D%0Ainfinitely many solutions%0D%0A%0D%0Atwo solutions%0D%0Atwo solutions%0D%0A%0D%0Aone solution%0D%0Aone solution%0D%0A%0D%0Ano solutions
1 answer