How do you solve the following system?: −2x−5y=1,−x−y=−2

1 Answer
Júlio B.
Apr 13, 2016

Just like this. It is a big answer but it is easy to understand

Explanation:

First, put one line above the other:
−2x−y=1
−x−y=−2

Now, we check if one line may delete(remainder = 0) any element from the other adding them:
−2x+(−x)=−3x⇒ No
−y+(−y)=−2y⇒ No
1+(−2)=−1⇒ No

Since add it has not deleted any element, multiply any of the lines by (-1) and try adding it again. I will chose the second line to multiply, its easier this way:
−2x−y=1⇒ −2x−y=1
−x−y=−2⇒ x+y=2

Adding:
−2x+x=−x⇒ No
−y+y=0⇒ Yes!
1+2=3⇒ No

Since this way one element was deleted (y), we may put it all in one "universal line":
−x+0=3 that becomes x=−3

To find y its way more simple, you just put the value of x in any place that he belongs to. Again I will chose the second line, still easier.
−(−3)−y=−2
−y+3=−2
−y=−5
y=5

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