SOLUTION: the sum of two numbers is two hundred thirty. their difference is sixty. what are the numbers? *SOLVE USING A SYSTEM OF EQUATIONS

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Question 46342: the sum of two numbers is two hundred thirty. their difference is sixty. what are the numbers? *SOLVE USING A SYSTEM OF EQUATIONS
Found 2 solutions by Nate, mszlmb:
Answer by Nate(3500)   (Show Source): You can put this solution on YOUR website!
a + b = 230
and
a - b = 60
Combine Them:
a + b = 230
+
a - b = 60
2a = 290
a = 145
plug:
a + b = 230
145 + b = 230
b = 85
Answer by mszlmb(115)   (Show Source): You can put this solution on YOUR website!
Let the two numbers be X and Y, X being the larger number if there is one.
X+Y=230
X-Y=60

Take the second equation:
X+Y=30  minus X on both sides
Y=230-X

Now solve by substitution:
We know Y=230-X from the first problem, so replace Y in the second problem by (230-X)

X-(230-X)=60  distribute the invisible -1
X-230+X=60  +230 on both sides
2X=290  divide by 2 on both sides
X=145

Knowing this, we go back to the second equation to replace X with 145 and get Y:
145-Y=60  minus 145 on both sides
-Y=-85  times -1 on both sides
Y=85

X=145
Y=85
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