What is the value of the product xy?

Question

I'm doing a practice test for the PSAT and I have a problem that I'm a little bit stuck on. Any help will be amazing!

The question is:

What is the value of the product xy?

4x-y=3y+7

x+8y=4

A) -3/2

B) 1/4

C) 1/2

D) 11/9

Answer 1

First, you want to solve the system of equations. A system of equations just means when you have two equations like this (you know it's an equation because of the equal sign in the middle), but you aren't given the values of x and y directly. That's why you have to solve the system!

This system has two equations:

4x-y=3y+7

x+8y=4

First, set them up so you have just one variable on each side. here's how I would do it:

4x = 4y + 7

x = y + 7/4

AND

x = 4 - 8y

Now you have two expressions for the value of x, (y + 7/4), and (4 - 8y). You know these are equal because, of course, x = x.

What happens if we put these two expressions into an equation, in which they are equal? Let's try it.

y + 7/4 = 4 - 8y

y = 9/4 - 8y

9y = 9/4

y = 1/4

Yay! Now we have a value for y. How do we find x? By plugging that value into the equation we have for x.

It's nicely set up:

x = 4 - 8y

x = 4 - 8*1/4

x = 4 - 2

x = 2

Awesome! Now we have a value for x, AND a value for y. All we have to do now is multiply them.

1/4 * 2 = 1/2

The answer is C, 1/2.