Question

question 1 of 10
find the value of q in the following system so that the solution to the system is \\{(x,y) : x - 3y = 4\\}.

x - 3y = 4
2x + qy = 8

Explanation:

Step1: Analyze the system of equations

The solution set of the system is \(\{(x,y):x - 3y=4\}\), which means the two equations are dependent (they represent the same line). So we can transform the first equation to match the second equation's form.

Step2: Multiply the first equation by 2

Multiply the equation \(x - 3y = 4\) by 2. We get \(2x-6y = 8\).

Step3: Compare with the second equation

The second equation is \(2x + Qy=8\). For the two equations to be the same (so that they have the same solution set), the coefficients of \(y\) must be equal. So comparing \(2x-6y = 8\) and \(2x + Qy=8\), we can see that \(Q=- 6\).

Answer:

\(Q = - 6\)