Question: Value of x in a System

Comment on Value of x in a System

How come you can't take one equation, solve for y in terms of x, and then substitute that y-value back into the equation and subsequently solve for x?
gmat-admin's picture

Try it, and you'll find a problem.

The reason you'll find a problem is that both equations are equivalent. That is, both equations can be written as 6x - 3y = -9 (or we could write both equations as 2x - y = -3).

So, we don't have two unique equations with 2 variable. Instead, we have ONE equation with 2 variables.

hi Brent, how did you know that the top equation had to multiplied by 1.5?

I derived the same conclusion when I solved the solved both the equations for x and I got the same result. But your approach is faster.
gmat-admin's picture

Great question!

Once we have....
4x - 2y = -6
6x - 3y = -9
.... I noticed that 6x = 1.5(4x) and 3y = 1.5(2y) and 9 = 1.5(6)

So, I knew that multiplying the top equation by 1.5 would yield equivalent equations.

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