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## Comment on

Number of Solutions to a System## @1.14 Can we just leave one

## When you multiply/divide both

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!

## Thanks Swatato!

Thanks Swatato!

## So is the answer a+b = -2?

## Exactly.

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

the answer should be A, as equation 1 and 2 are not equivalent?

## Question link: https:/

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!

## Question link: https:/

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!

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