Question

Question 5 of 6Identify the augmented matrix for the system of equations and the solution using row operations. 6x − 5y = 37 4x + 9y = 0 Identify the augmented matrix for the system of equations and the solution using row operations. 6x − 5y = 37 4x + 9y = 0

Answer 1

The augmented matrix for the system 6x − 5y = 37 and 4x + 9y = 0 is [[6, -5, 37], [4, 9, 0]]. To solve it using row operations, we perform a series of steps to achieve an upper triangular matrix and then use back-substitution to find the values of x and y.

Step-by-step explanation:

To identify the augmented matrix for the system of equations 6x − 5y = 37 and 4x + 9y = 0, we write the coefficients and the constants in a matrix form. The matrix has two rows, corresponding to each equation, and three columns, corresponding to the coefficients of x, the coefficients of y, and the constant term on the right side of the equation.

The augmented matrix is therefore: [[6, -5, 37], [4, 9, 0]].

Now, to find the solution using row operations, we can perform the following steps:

1. Multiply the second row (R2) by 1.5 and subtract it from the first row (R1) to eliminate the x-term from R1. This gives us a new R1.
2. Next, we can scale R2 to make the coefficient of y the leading 1 if necessary.
3. Perform additional row operations to achieve an upper triangular matrix, where the lower left corner below the main diagonal contains only zeroes.
4. Finally, use back-substitution to find the values of x and y.

The exact row operations will depend on the resulting matrix after each step. Generally, the goal is to achieve a matrix that is easy to use for back substitution. The solution will be of the form (x, y), representing the intersection of the two lines represented by the original system of equations.