Questions: QUESTION 7 • 1 POINT Use the most convenient method to solve the following system of equations. ⎨3x + 4y = 10 ⎩4x + 3y = 1 Write your answer as an ordered pair in the form (x, y). Provide your answer below:

Solution Steps

To solve the system of equations, we can use the method of substitution or elimination. Here, the elimination method is more convenient. We will multiply each equation by a suitable number to make the coefficients of one of the variables equal, then subtract one equation from the other to eliminate that variable. Finally, we solve for the remaining variable and substitute back to find the other variable.

We start with the given system of equations: \[ \begin{cases} 3x + 4y = 10 \\ 4x + 3y = 1 \end{cases} \]

We represent the system in matrix form \(A \mathbf{x} = \mathbf{b}\), where: \[ A = \begin{bmatrix} 3 & 4 \\ 4 & 3 \end{bmatrix}, \quad \mathbf{b} = \begin{bmatrix} 10 \\ 1 \end{bmatrix} \]

Using linear algebra techniques, we solve for \(\mathbf{x}\): \[ \mathbf{x} = A^{-1} \mathbf{b} \]

The solution to the system is: \[ \mathbf{x} = \begin{bmatrix} -3.7143 \\ 5.2857 \end{bmatrix} \]

Final Answer