Questions: Find the value of Q in the following system so that the solution to the system is (x, y): x-3 y=4. x-3 y=4 2 x-6 y=Q

Solution Steps

We are given the following system of equations:

\[ \begin{array}{l} x - 3y = 4 \\ 2x - 6y = Q \end{array} \]

To find the value of \( Q \) such that the solution to the system is consistent with the first equation, we can express the second equation in terms of the first.

The second equation can be derived from the first by multiplying it by 2:

\[ 2(x - 3y) = 2 \cdot 4 \implies 2x - 6y = 8 \]

Thus, for the system to have the same solution, we must have \( Q = 8 \).

We can represent the system in augmented matrix form:

\[ \left[ A | b \right] = \left[ \begin{array}{ccc} 1 & -3 & 4 \\ 2 & -6 & 8 \\ \end{array} \right] \]

After performing Gaussian elimination, we find:

\[ \left[ A | b \right] = \left[ \begin{array}{ccc} 1 & -3 & 4 \\ 0 & 0 & 0 \\ \end{array} \right] \]

This indicates that the second equation does not provide any new information, leading to infinite solutions.

Final Answer