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Suppose a, b, c, and d are real numbers which satisfy the system of equations

a + 2b + 3c + 4d = 10

4a + b + 2c + 3d = 4

3a + 4b + c + 2d = -10

2a + 3b + 4c + d = −4.

Find a + b + c + d.

 May 2, 2022
 #1
avatar+2440 
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Adding all 4 equations gives us: \(10(a+b+c+d)=0\)

 

Dividing both sides by 10, we find \(a+b+c+d=\color{brown}\boxed{0}\)

 May 2, 2022
 #2
avatar+117841 
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Hi Builderboi,

 

Thanks for all your great answers.

 

I do have a suggestion though.

Try experimenting with giving answers that encourage askers to learn and that make it more difficult for them to just copy.

 

Like here you could have said.

"Try adding all the left sides and putting the answer equal to the sum of all the right sides.  See what you get ;)"

 

People are much more likely to learn from you if you do not do all the work for them.

Teaching is a learned art.  laugh

 May 2, 2022

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