SOLUTION: I do not know where to start. When do you multiply numbers to the x and y. my problem is this 2x+y = 5 -6x - 3y = -15 My teacher said that you multiply the 2x and the y by 3

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Question 188345: I do not know where to start. When do you multiply numbers to the x and y.
my problem is this
2x+y = 5
-6x - 3y = -15 My teacher said that you multiply the 2x and the y by 3 why? and how do you finish after that?
Found 3 solutions by Alan3354, Earlsdon, solver91311:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website!
I do not know where to start. When do you multiply numbers to the x and y.
my problem is this
2x+y = 5
-6x - 3y = -15 My teacher said that you multiply the 2x and the y by 3 why? and how do you finish after that?
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In order to eliminate one of the variables, you multiply one of the equations by something to get the same coefficients. In this case, multiplying the 1st eqn by 3 gives 6x + 3y = 15. The coeff's for x and y are the same as in the other equation. That's the reason to multiply by 3.
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In this example, tho, the 2 equations are actually the same. If you add them (after multiplying by 3) you get 0x + 0y = 0.
There is no unique solution for this pair of eqns.
If you graph them, you get the same line 2 times.

Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website!
Solve:
1)
2)
The goal is to get both equations to have the same number of one of the variables (x or y), so if you multiply equation 1) by 3 you can then add the two equations to eliminate the x-variable allowing you to solve for y.
Take a look!
1) Multiply both sides of this equation by 3.
1a)
1b) Now add this equation to equation 2):
1a)
2)
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3) So the two sides are equal but both of the variables disappeared. This means that the graphs of the two equations coincide (they produce the same line) and so there are an infinite number of solutions.
The system is said to be a "consistent sytem" because it has at least one solution, and the equations are said to be "dependent equations".

Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!

I certainly hope that your teacher did not tell you to multiply only the 2x and the y by 3. Because if

then

You need to multiply both sides of the first equation by 3 to get:

The reason you are doing that is so that the coefficients on the x terms in the two equations become additive inverses, that is you want the two coefficients to sum to zero. Here, 6 + (-6) = 0.

Your next step is to add the two equations term-by-term:

The two x terms: 6x + (-6x) = 0x

The two y terms: 3y + (-3y) = 0y

And the two constant terms: 15 + (-15) = 0

Leaving you with the triviality: 0 = 0

What this means is that you have two equations that are representations of the same line in . The solution set for the two equations are identical, hence you have an infinite number of ordered pairs that satisfy both equations simultaneously.

John