SOLUTION: the sum of a certain number and a second number is -42. the first number minus the second is 52. find the numbers.

Question 641139: the sum of a certain number and a second number is -42. the first number minus the second is 52. find the numbers.
Answer by josh_jordan(263) (Show Source): You can put this solution on YOUR website!
To solve, let's turn each of the sentences into an equation. The first sentence says that the sum of a certain number and a second number is -42. In other words:
x + y = -42 (where x and y each represent one of those numbers)
The second sentence says that the first number minus the second number is 52. In other words:
x - y = 52
These two equations form a system of linear equations. We can find x and y by adding these two equations together. So,
x + y + x - y = -42 + 52
Leaving us with
2x = 10
Dividing both sides by 2 will leave us with x:
, so
x = 5
Now, to solve for y, just replace x in either equation, with 5. Let's use the first equation: x + y = -42:
5 + y = -42
Subtract both sides by 5:
5 - 5 + y = -42 - 5, so
y = -47
FINAL ANSWER: 5 and -47 are the two numbers
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