Lesson: Number of Solutions to a System

Comment on Number of Solutions to a System

@1.14 Can we just leave one equation multiplied by 2, do we have to multiply both the equation by 2 to give them equality.
gmat-admin's picture

When you multiply/divide both sides of an equation by some value, you are creating an EQUIVALENT equation. For example, the equation x + y = 3 is EQUIVALENT to the equation 2x + 2y = 6

So, to answer your question, you need not multiply both EQUATIONS by 2.

Beautifully explained!
gmat-admin's picture

Thanks Swatato!

So is the answer a+b = -2? Since a cannot equal b. Cheers beforehand! :)
gmat-admin's picture

Exactly.
When we solve each equation we get:
a = -6 OR a = 4
b = -6 OR b = 4

Since a ≠ b, we know that one solution is -6 and the other solution is 4
So, a + b must equal -2

Cheers,
Brent

Hi, for this question link https://gmatclub.com/forum/the-system-of-equations-has-how-many-solutions-279317.html

the answer should be A, as equation 1 and 2 are not equivalent?
gmat-admin's picture

Question link: https://gmatclub.com/forum/the-system-of-equations-has-how-many-solution...

You're absolutely right. For some reason, I was solving a completely different system of equations.
I have edited my solution accordingly.

Thanks for the heads up!

gmat-admin's picture

Question link: https://gmatclub.com/forum/the-system-of-equations-has-how-many-solution...

You're absolutely right. For some reason, I was solving a completely different system of equations.
I have edited my solution accordingly.

Thanks for the heads up!

Add a comment

Office Hours

Have questions about your preparation or an upcoming test? Need help modifying the Study Plan to meet your unique needs? No problem. Just book a Skype meeting with Brent to discuss these and any other questions you may have. 

Change Playback Speed

You have the option of watching the videos at various speeds (25% faster, 50% faster, etc). To change the playback speed, click the settings icon on the right side of the video status bar.

Have a question about this video?

Post your question in the Comment section below, and I’ll answer it as fast as humanly possible.

Free “Question of the Day” emails!