Question

I need a verbal answer:D so a sentence I'd appreciate any help

Answer 1

3x + 6y = 9
9x + 18y = 27

The two equations above may or may not be equivalent. So let's try to solve it.
The first impulse is to multiply the first equation by -3 to eliminate the x variable. When doing that we get:

-3(3x + 6y = 9)
9x + 18y = 27

Distributing -3 across the first equation, we get:
-9x - 18y = -27
9x + 18y = 27
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We now know the two equations are equivalent since the second equation is just a multiple of the first equation. To see it more clearly, lets observe the original system again:


3x + 6y = 9
9x + 18y = 27

In the second equation, 3 is common to each term so factor it out:

3x + 6y = 9
3(3x + 6y = 9)

Now it is clearly seen that the second equation is a multiple of the first. Thus both equations will have the same solution.

Answer 2

I just showed you how it is easier. All you do is factor out common factors and then observe that they are equivalent:

Two mathematical sentences (equations)

3x + 6y = 9
9x + 18y = 27

Factor 3 out of second equation:

3x + 6y = 9
3(3x + 6y = 9)

This is the easiest way to observe equivalent equations

Answer 3

Thx got it :D