Question

question 9 of 10 find the value of q in the following system is \\{ (x,y) : x - 3y = 4 \\}. x - 3y = 4 2x - 6y = q

Explanation:

Step1: Analyze the system of equations

The first equation is \(x - 3y = 4\). The second equation is \(2x - 6y = Q\). Notice that the second equation can be factored.

Step2: Factor the second equation

Factor out a 2 from the left - hand side of the second equation: \(2x-6y = 2(x - 3y)\).

Step3: Substitute the first equation into the factored form

Since from the first equation we know that \(x - 3y=4\), we substitute \(x - 3y\) with 4 in the expression \(2(x - 3y)\). So \(2(x - 3y)=2\times4\).

Step4: Calculate the value of Q

Since \(2x - 6y = Q\) and \(2x - 6y=2(x - 3y) = 2\times4 = 8\), we can conclude that \(Q = 8\).

Answer:

\(Q = 8\)