SOLUTION: Write the system of equations that has (3.-4) as its only solution and both lines are perpendicular to each other. I solved this problem like this but I am not sure if this is cor

Algebra ->  Linear-equations -> SOLUTION: Write the system of equations that has (3.-4) as its only solution and both lines are perpendicular to each other. I solved this problem like this but I am not sure if this is cor      Log On


   

Question 1165538: Write the system of equations that has (3.-4) as its only solution and both lines are perpendicular to each other.
I solved this problem like this but I am not sure if this is correct way of thinking. Thank you.
My solution: x+y=c, 3+(-4)=3-4=-1,
x-y=d, 3-(-4)=3+4=7,
My system of equation is:
y=-x-1
y=x-7
Both lines are perpendicular because -1times1=-1
Thank you.
Answer by ikleyn(52903) About Me  (Show Source):
You can put this solution on YOUR website!
.

Your answer is correct.


But it is not a unique answer.


It is not a unique answer, because there is more than one pair of such straight lines.


For example, the pair (the system of equation)

    x= 3

    y= -4

is another pair (another system of equations).


Any system of equations (and any pair of perpendicular lines) that obtained from your pair (or from my pair) by a rotation 

to an arbitrary angle about the center (3,-4) satisfies the given conditions/requirements, too.