Question

Solve 2a + 6b = -1 and a + 8b = 2 using Cramer's rule.

Answer 1

Using Cramer's rule, the values for 'a' and 'b' in the system of equations are found to be a = -2 and b = 0.5.

Step-by-step explanation:

To solve the system of equations 2a + 6b = -1 and a + 8b = 2 using Cramer's rule, we need to find the determinant of the coefficient matrix (D) and the determinants of the matrices formed by replacing the respective columns with the constants from the right-hand side, called Da and Db.

The coefficient matrix and its determinant (D) are:

• | 2 6 |
• | 1 8 |

Which gives us D = (2)(8) - (6)(1) = 16 - 6 = 10.

The determinant Da when replacing the first column with the constants is:

• | -1 6 |
• | 2 8 |

So, Da = (-1)(8) - (6)(2) = -8 - 12 = -20.

The determinant Db when replacing the second column with the constants is:

• | 2 -1 |
• | 1 2 |

Thus, Db = (2)(2) - (-1)(1) = 4 + 1 = 5.

Now we can find the values for 'a' and 'b' using the formulas:

• a = Da / D = -20 / 10 = -2
• b = Db / D = 5 / 10 = 0.5

Therefore, the solution of the system is a = -2 and b = 0.5.