Question

Find the value of Q in the following system so that the solution to the system is {(x,y) : x-3y=4}

Answer 1

x-3y=4

Explanation:

Answer 2

Explanation

We have a pair of equations and we are told that the solution to this system is the equation:

`x-3y=4`

This implies that the system has infinite solutions so one of the equations must be a multiple of the other. We are going to take the first equation and multiply both of its sides by a number k and then compare the result with the second equation:

`\begin{gathered} k\cdot(x-3y)=k\cdot4 \\ kx-3ky=4k\leftrightarrow2x-6y=Q \end{gathered}`

Now let's compare the left sides of this equations. If k=2 then the teo left sides are the same expression. So the second equation must be the first equation multiplied by 2. Then the value of Q is:

`\begin{gathered} Q=4k=4\cdot2 \\ Q=8 \end{gathered}`

So with Q=8 the second equation is a multiple of the first and the solution of the system is the one requested.

Answer

Then the answer is 8.