Question

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

Answer 1

1) First eqation x-3y=4 2) 2x+qy=8 It looks like if first equations is multiplied by 2 we get second equation, So let do it 2x-6y=8 So we see that in place of q is -6

Answer 2

If the solution of the system is {(x,y) : x-3y=4}, then both equation should have proportional coefficients:

`(1)/(2)=(-3)/(q)=(4)/(8).`

Solve it:

`(1)/(2)=(-3)/(q),\\ \\1\cdot q=-3\cdot 2,\\q=-6.`

Check whether q=-6 is correct answer, substituting this value into the first ratio:

`(1)/(2)=(-3)/(-6)=(4)/(8).`

Answer: q=-6.