Answer:
3
Step-by-step explanation:
You want the value of (x+y) as determined by the system of equations ...
Solution
We can subtract the second equation from the first to get ...
(y) -(y) = (3x -1) -(-2x +4)
0 = 5x -5
0 = x -1
1 = x
Using the first equation to find y, we have ...
y = 3(1) -1 = 2
The sum of x and y is (x +y) = (1 +2) = 3.
Alternate solution
Let t = x+y. This means y = t -x.
Now, the equations become ...
- t -x = 3x -1
- t -x = -2x +4
Adding 4 times the second equation to the first gives ...
(t -x) +4(t -x) = (3x -1) +4(-2x +4)
5t -5x = -5x +15
Adding 5x and dividing by 5 gives ...
t = 3
The sum of x and y is 3.
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Additional comment
Sometimes you can find the value of the objective function directly, as in the second solution here.
The reason we chose 4 as a multiplier in the alternate solution is that we observed the equations could be written as ...
t -4x = -1
t +x = 4
where the variable x has coefficients with a ratio of -4. Using 4 as the multiplier eliminates the x-variable, leaving t — the variable whose value we want.
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