System of Equations Involving a Quadratic: Have Answer <> Understand

[kwixson]

Homework Statement

Solve this system of equations for x and y.

v=x+y
v^2=x^2+y^2

Homework Equations

The quadratic formula:

x = (-b +/- sqrt(b^2-4*a*c))/(2*a)

The Attempt at a Solution

A TA gave the following advice:

"Make y the subject of the first equation.
Find y2 in terms of v and x using this equation.
Substitute y2 in the second equation.
You now have a quadratic equation in x and there will be two solutions"​

I know the answers are x=0 and y=v but I "can't get there from here." My most recent attempt I got as far as 2x^2-2vx=0.

In this case, this homework is already solved so if someone could walk me through it I would be grateful.

 

[Mark44]

Homework Statement

Solve this system of equations for x and y.

v=x+y
v^2=x^2+y^2

Homework Equations

The quadratic formula:

x = (-b +/- sqrt(b^2-4*a*c))/(2*a)

The Attempt at a Solution

A TA gave the following advice:

"Make y the subject of the first equation.
Find y2 in terms of v and x using this equation.
Substitute y2 in the second equation.
You now have a quadratic equation in x and there will be two solutions"​

I know the answers are x=0 and y=v but I "can't get there from here." My most recent attempt I got as far as 2x^2-2vx=0.

In this case, this homework is already solved so if someone could walk me through it I would be grateful.

I would do something different from what your TA suggested. The first equation is v = x + y. I would substitute substitute x + y for v in the second equation, to get (x + y)² = x² + y².

Expand the left side and simplify. What do you get?

 

[Office_Shredder]

I know the answers are x=0 and y=v but I "can't get there from here." My most recent attempt I got as far as 2x^2-2vx=0.

So is your question just how to solve this quadratic equation really? Because you can easily factor it
2x(x-v) = 0

So what are the possibly solutions?