Question

Find the value of Q in the following system so that the solution to the systemIs{(x, y) : x – 3y =4}x-3y=42x + Qx=8

Answer 1

Since the solution of the system is any point (x, y) where the relation between x and y is given by the equation x - 3y = 4, that means the system has an infinite number of solutions, therefore the second equation of the system is a line paralell to the line of the first equation.

Calculating the slope of each equation, we have:

`\begin{gathered} x-3y=4 \\ 3y=x-4 \\ y=(x)/(3)-(4)/(3)\to\text{slope}=(1)/(3) \\ \\ 2x+Qy=8 \\ Qy=-2x+8 \\ y=(-2x)/(Q)+(8)/(Q)\to slope=-(2)/(Q) \end{gathered}`

Since the lines are paralell, they have the same slope, so:

`\begin{gathered} (1)/(3)=-(2)/(Q) \\ Q=-2\cdot3 \\ Q=-6 \end{gathered}`