Write as a Vector Equality x+y=6 , x/y=2

Problem

{[x+y=6],[x/y=2])

Solution

1. Rearrange the second equation to remove the fraction by multiplying both sides by y

x=2*y

2. Rewrite both equations in standard form a*x+b*y=c so that the variables align.

1*x+1*y=6

1*x−2*y=0

3. Express the system as a linear combination of constant vectors scaled by the variables x and y

x*[[1],[1]]+y*[[1],[−2]]=[[6],[0]]

Final Answer

{[x+y=6],[x/y=2])⇒x*[[1],[1]]+y*[[1],[−2]]=[[6],[0]]

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