solve 2x+y=5 if x and y are whole numbers?

Question

{(0, 5), (1, 3), (2, 1)}


{(0, 5), (1, 4), (2, 1)}


{(0, 5), (1, 3), (2, 1)}


{(0, 5), (1, 4), (2, 1)}

Answer 1

Is it not obvious? 2 times the first number plus the second number must add to 5 exactly. Which line only has pairs that meet this criterion?

Answer 2

2x + y = 5

The bigger challenge is finding ALL whole number solutions to 2x + y = 5. {Note: I'm aware this isn't being asked but figure I would post it anyway, for information purposes. I don't really care about getting the best answer.}

This is a linear diophantine equation, but instead of integers, we want whole numbers. (integers 0 or greater).

Note that (2)(0) + 1 = 1, so multiply both sides by 5,

(2)(0) + (1)(5) = 5

One whole number solution to 2x + y = 5 is

x = 0
y = 5

This means our general solution is

x = 0 - k
y = 5 + 2k

Or, quite simply,

x = -k
y = 5 + 2k for some integer k.

Since x >= 0 and y >= 0 must be true, then

-k >= 0 and 5 + 2k >= 0. Solving these two inequalities individually,

-k >= 0. Multiply both sides by (-1) switches the inequality, into

k <= 0

5 + 2k >= 0
2k >= -5
k >= -5/2, or
k >= -2.5

k <= 0 and k >= -2.5 (with k being an integer) means
k = -2, -1, 0

So we have a total of THREE sets of solutions for x and y.

x = -k
y = 5 + 2k

k = -2:

x = -(-2) = 2
y = 5 + 2(-2) = 5 - 4 = 1

k = -1:

x = -(-1) = 1
y = 5 + 2(-1) = 5 - 2 = 3

k = 0:

x = 0
y = 5

All solutions:

x = 2, y = 1
x = 1, y = 3
x = 0, y = 5

Answer 3

The easy way is to try all the proposed answers. In each pair of numbers, the first one represents a value for x, the second one is the corresponding value for y.

For example, if we try (1,4), then we replace x with 1 and y with 4:

2x + y ?=? 5
2*1 + 4 ?=? 5
2 + 4 ?=? 5
FALSE

Therefore (1,4) is not a solution.


The correct answer is the line where ALL proposed solutions are true. In our example, above, we have shown that (1,4) is false, therefore we have eliminated that line. Once you have found one element that is false, you do not need to test the others in the same set.

However, to prove that a set is the answer, you must test every pair in it.

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PS: while it is true that there could be other answers, the question does not ask you to find all possible answers. It only asks you to choose among a list. So, only check the list. You do not have to check the entire universe...

Answer 4

{(0, 5), (1, 3), (2, 1)}

Answer 5

its (0, 5), (1, 4), (2, 1)

Answer 6

x=1, y=3....u gave all the answers already...why do u ask?

Answer 7

infinite solutions, unless you restrict to positive whole numbers.

Answer 8

{ (0,5),(1,3),(2,1)}