The following two vectors satisfy the same system of linear equations. u=⎡⎣⎢⎢6−5−5⎤⎦⎥⎥, v=⎡⎣⎢⎢746⎤⎦⎥⎥ Find x and y that make the vector ⎡⎣⎢⎢3xy⎤⎦⎥⎥ a solution to the corresponding homogeneous system:

x=-30/71, y=0

Step-by-step explanation:

if a vector satisfies an equation of the form ax+by+cz=0 then the vector is  

parallel to the plane ax+by+cz=0, and, the cross product of two vectors results in an orthogonal vector to both.

So, <a,b,c> the normal vector of the plane ax+by+cz=0, can be found as the cross product of the two parallel vetors to the plane:

<a,b,c> = <6,-5,-5>×<7,4,6>= <-10,-71,59>

so, the homogeneous system is:

-10x-71y+59z=0

by replacing the vector <3,x,y> in the system

-30-71x+59y=0

So, there are 2 unknown variables and 1 equation, it means that 1 variable is free

so, y=0 is a random defition and x can be obtain with the equation

-30-71x=0 -> x=-30/71

typically if you want , you would actually put questions here for us to you. but hey, that's just me. maybe someone will magically answer the questions for you without knowing what they are.

the reporter's right

step-by-step explanation:

1/4 = .25 / 25%