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Use matrix method to solve
2x-3y=-17
5x+6y=-2

User Patrics
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Answer and Step-by-step explanation:

To solve the system of equations using the matrix method, we can represent the equations in matrix form.

First, let's write the system of equations:

2x - 3y = -17 (Equation 1)

5x + 6y = -2 (Equation 2)

Next, we can represent the coefficients and constants of the equations in matrix form:

| 2 -3 | | x | = | -17 |

| 5 6 | | y | | -2 |

Now, let's write the augmented matrix, which combines the coefficient matrix and the constant matrix:

| 2 -3 -17 |

| 5 6 -2 |

To solve the system, we will perform row operations to transform the augmented matrix into row-echelon form or reduced row-echelon form.

Step 1: Divide Row 1 by 2 to make the leading coefficient of the first row 1:

| 1 -3/2 -17/2 |

| 5 6 -2 |

Step 2: Replace Row 2 with Row 2 - 5 * Row 1:

| 1 -3/2 -17/2 |

| 0 21/2 33/2 |

Step 3: Divide Row 2 by 21/2 to make the leading coefficient of the second row 1:

| 1 -3/2 -17/2 |

| 0 1 3 |

Step 4: Replace Row 1 with Row 1 + (3/2) * Row 2:

| 1 0 -2 |

| 0 1 3 |

The augmented matrix is now in reduced row-echelon form. The leftmost column represents the coefficients of x and y, respectively, while the rightmost column represents the constant terms.

From the reduced row-echelon form, we can read the solution of the system:

x = -2

y = 3

Therefore, the solution to the system of equations is x = -2 and y = 3.

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