Given:
x - y = -10
x² - 2xy = 84


Take top equation and square both sides to get: (x - y)² = (-10)²
Expand and simplify: to get: x² - 2xy + y² = 100

We now have:
x² - 2xy + y² = 100
x² - 2xy = 84

Subtract bottom equation from top equation to get: y² = 16
So, EITHER y = 4 OR y = -4

In both cases, |y| = 4

Answer: 4

Cheers,
Brent

Another approach is to use substitution

Given:
x - y = -10
x² - 2xy = 84

Solve the top equation for x to get: x = y - 10

Take the bottom equation and replace x with (y - 10) to get: (y - 10)² - 2(y - 10)y = 84
Expand left side to get: y² - 20y + 100 - 2y² + 20y = 84
Simplify: -y² + 100 = 84
Subtract 100 from both sides to get: -y² = -16
Divide both sides by -1 to get: y² = 16
Solve: y = 4 OR y = -4

In both cases, |y| = 4

Answer: 4

Cheers,
Brent

If \(x^2 - 2xy = 84\) and \(x - y = -10\), what is the value of \(|y|\)?

We know that \((x-y)^2 = x^2 + y^2 - 2xy\)

\(x^2 - 2xy = (x-y)^2 - y^2\)

\(84 = (-10)^2 - y^2\)

\(84 - 100 = -y^2\)

\(-36 = -y^2\)

\(36 = y^2\)

\(y^2 = 36\)

\(y=\pm {4}\)

\(|y| = 4\)

Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.