Question

Consider the following system of linea equations - 5x+10y-30 --6x +17y21 solve the system by completing the steps below to produce a reduced row echelon form., and R, denote the first and secondes, rectively. The notation (-) means the expression/matrix on the left becomes the expressmatra on the right once the rowers are performed 00:01 (a) Enter the augmented matrix bio (b) for each step below, enter the coefficient for the row operation and the mig entries in the resulting matrix

Answer 1

To solve the system of linear equations, we can use row operations to transform the augmented matrix into reduced row echelon form. The solution to the system of equations is x = 0 and y = -2.11.

Step-by-step explanation:

To solve the system of linear equations, we can write the augmented matrix using the coefficients of the variables and constant terms. The augmented matrix for the given system is:

| -5 10 -30 |

| -6 17 21 |

To reduce the matrix to its row echelon form, we can perform row operations. The goal is to transform the matrix into an upper triangular form. Here are the steps:

1. Multiply the first row by 6 and the second row by 5, then add the second row to the first row:
2. | -30 60 -180 ||
3. 0
4. 85 -179 |
5. Divide the second row by 85 to make the leading coefficient 1:
6. | -30 60 -180 || 0
7. 1
8. -2.11 |
9. Multiply the second row by -60 and add it to the first row:
10. |
11. 0
12. 0 0 || 0 1 -2.11 |

The matrix is now in reduced row echelon form. The solution to the system of equations is x = 0 and y = -2.11.

Learn more about Solving systems of linear equations