SOLUTION: the problem is 1/5x+1/5y=1 x-y=1 i multiplied the top equation by 5 to eliminate the fractions and got: x+y=5 x-y=1 just not quite sure where to go from here to solv

Question 665679: the problem is
1/5x+1/5y=1
x-y=1
i multiplied the top equation by 5 to eliminate the fractions and got:
x+y=5
x-y=1
just not quite sure where to go from here to solve?
Found 2 solutions by ReadingBoosters, DrBeeee:
Answer by ReadingBoosters(3246) (Show Source): You can put this solution on YOUR website!
Now, add them together...
x+y=5
x-y=1
...
x + x + y + -y = 5 + 1
Combine like terms
2x = 6

...
Multiply the second equation by -1 to get -x+y=-1
Add them together
x + -x +y + y = 5 + -1
Combine like terms
2y = 4

...
Check

.....................
Delighted to help.
-Reading Boosters
Wanting for others what we want for ourselves.
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Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
I love your first step as I hate fractions!
Your system of equations are
(1) x + y = 5
(2) x - y = 1
There are 2 or 3 ways to solve a pair of equations like these. I'll give you a couple, then which one you use depends on the simplicity of the given pair.
The first is harder to understand by a beginner, but in this problem it is an obvious way to solve them. It is to add or subtract the equations from each other. Look at (1) and (2), see how the x terms and y terms are aligned under each other? The first technique is to recognized that if I literally ADD the left sides of (1) and (2) we get
(3) x + y + x - y
and if we add the right sides of (1) and (2) we get
(4) 5 + 1
Equating (3) and (4) we get
(5) 2x + 0 = 6 or
(6) x = 3 and using (1) we get
(7) 3 + y = 5 or
(8) y = 2
We'll show that (3,2) is the solution pair below, but now I want to show you the substitution method.
Using substitution, we solve one of the given equations for one of the variables in terms of the other variable. Then substitute the resulting expression into the second equation. Easier to do than explain so let's do it.
Solve (2) for x and get
(9) x = 1 + y
Now put this expression for x into (1) giving us
(10) 1 + y + y = 5 or simplifying
(11) 2y = 4 or
(12) y = 2 as before.
Now put (12) into (9) and get
(13) x = 1 + 2 or
(14) x = 3
Again the solution pair is (3,2).
Is this correct?
To check go back to the original (before you multiplied by 5) given equations. Is (3/5 + 2/5 = 1)?
Is (5/5 = 1)?
Is (1 = 1)? Yes
Is (3 - 2 = 1)?
Is (1 = 1)? Yes
Answer: The solution pair is (3,2).

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