Questions: Exercise 7.7 Solve. 3x + 2y = 6 6x + 4y = 16

Solution Steps

To solve the system of linear equations, we can use matrix operations or a solver function from a library like NumPy. The equations can be represented in matrix form \(AX = B\), where \(A\) is the coefficient matrix, \(X\) is the variable matrix, and \(B\) is the constant matrix. We can then use NumPy's linalg.solve function to find the values of \(x\) and \(y\).

We start with the given system of linear equations: \[ \begin{array}{l} 3x + 2y = 6 \\ 6x + 4y = 16 \end{array} \]

Notice that the second equation can be simplified by dividing every term by 2: \[ 6x + 4y = 16 \implies 3x + 2y = 8 \]

Now we have the simplified system: \[ \begin{array}{l} 3x + 2y = 6 \\ 3x + 2y = 8 \end{array} \]

We observe that the two equations are: \[ 3x + 2y = 6 \quad \text{and} \quad 3x + 2y = 8 \] These two equations are contradictory because the same linear combination of \(x\) and \(y\) cannot equal two different constants (6 and 8).

Final Answer