To solve the system of equations using Cramer’s Rule, we first need to express the system in standard form. The equations you provided seem to be incomplete or unclear. However, based on the consistent format they follow, I will assume you meant:
1. 3x + y = 19
2. 3x + y = 23
First, let’s note that we have the two equations:
Equation 1: 3x + y = 19
Equation 2: 3x + y = 23
Next, we need to find the determinant of the coefficient matrix (D). This matrix contains the coefficients of x and y:
D = | 3 1 |
| 3 1 | = (3 * 1) – (1 * 3) = 3 – 3 = 0
Now, we also need the determinants for Dx and Dy. However, since D = 0, we can already conclude something important:
When the determinant of the coefficient matrix (D) is zero, it indicates that the system of equations is either dependent (infinitely many solutions) or inconsistent (no solution). In our case, since both equations represent the same line, they are dependent, and thus there are infinitely many solutions along that line.
To summarize, using Cramer’s Rule, we confirmed:
- The determinant D = 0
- Indicating the lines represented by the equations are parallel, thus having no unique solution.
Therefore, the system has infinitely many solutions represented by the line 3x + y = 19 (or 3x + y = 23, as they are the same).