9514 1404 393
Answer:
(x, y) = (3, 9)
Explanation:
When you add the two equations together, you get ...
(y) +(y) = (2x +3) +(-2x +15)
2y = 18 . . . . . . simplify
y = 9 . . . . . . . . divide by 2
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When you subtract the second equation from the first, you get ...
(y) -(y) = (2x +3) -(-2x +15)
0 = 4x -12 . . . . . simplify
0 = x -3 . . . . . . . divide by 4
3 = x . . . . . . . . . add 3
The solution is (x, y) = (3, 9).
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Additional comments
These are two equations in two unknowns. There are a number of ways to solve them. One of the simplest is to use one expression for y to substitute for y in the other equation:
2x +3 = -2x +15
Adding 2x and subtracting 3*, you get
4x = 12
x = 3 . . . . same solution as above.
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* As with any operation performed on an equation, you must do the same thing to both sides of the equation. For example, "adding 2x" looks like ...
2x +3 +2x = -2x +15 +2x . . . . . "2x" is added to both sides of the equation
When we collect terms, this simplifies to ...
4x +3 = 15 . . . . . note that -2x+2x = 0