Inopeki
Can someone teach me systems of equations?



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agdgdgdgwngo
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a linear system is simply a set of linear equations.

Inopeki
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Ok, but can you give me an example so i can try?

agdgdgdgwngo
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here's an easy one:
2x + y = 3
x + y = 1

Inopeki
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2x + y = 3
+ x + y = 1
Is this the right first step?

agdgdgdgwngo
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you can do 3 different things to solve a linear system:
1. graph the equations, and find where they intersect.
2. substitution
3. elimination.

Inopeki
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Im gonna do elimination then substitution

Inopeki
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No wait

Inopeki
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I cant do elimination on this one

Inopeki
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2x + y = 3
+ x + y = 12y
3x=42y

Inopeki
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That cant be right

agdgdgdgwngo
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you can; in fact elimination would be the easy way out of this one

Inopeki
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WAIT

Inopeki
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Can i divide the equations?

agdgdgdgwngo
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if you subtract equation 2 from equation 1: you get
x = 2
x + y = 1
next step is to subtract the new equation 1 from equation 2

Inopeki
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y=1?

agdgdgdgwngo
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you can't really divide the equations

Inopeki
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Ok, i see why now

Inopeki
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Give me another one so i can try, i think i see the pattern

agdgdgdgwngo
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2x + y = 5
x + y = 3

Inopeki
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2x + y = 5  x + y = 3 = x=2? The y's cancel out right?

Inopeki
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Now i can substitute to get y

agdgdgdgwngo
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right

Inopeki
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2 + y = 3
y=1

Inopeki
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I can cross check this with the other equation

Inopeki
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4 + 1 = 5
2 + 1 = 3