How do you solve the following system?: -2x -3y =-3, 4x -5y = -4−2x−3y=−3,4x−5y=−4

1 Answer
Roy Ø.
Jun 8, 2018

x=3/22, y=10/11x=322,y=1011

Explanation:

You have the system:
1) -2x-3y=-3−2x−3y=−3
2) 4x-5y=-44x−5y=−4

Multiply 1) with 2 and add the resulting equation to 2), like this:
-4x-6y=-6−4x−6y=−6
4x-5y=-44x−5y=−4
Adding these together term by term, we get:
-11y=-10−11y=−10

=>y=10/11⇒y=1011
From 1) we get:
2x=-3y+3=-30/11+3=3/112x=−3y+3=−3011+3=311
x=3/22x=322

It is always a good idea to use the results found and put them into the original system:

1) -2x-3y=-2*3/22-3*10/11=-(6+60)/22=-3−2x−3y=−2⋅322−3⋅1011=−6+6022=−3 Check
2) 4x-5y=4*3/22-5*10/11=(6-50)/11=-44x−5y=4⋅322−5⋅1011=6−5011=−4 Check

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