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Question 895201: There are two mystery numbers. The sum of 3 times the first number and 7 times the second number is -10. The sum of 4 times the first number and 6 times the second number is -10. What are the two numbers?
Answer by JulietG(1812)   (Show Source):
You can put this solution on YOUR website! Let x be the first number, and y be the second.
3x +7y = -10
4x +6y = -10
The equations are equal to each other so they can be set against each other.
3x+7y = 4x+6y
Subtract 3x from each side
7y = x + 6y
Subtract 6y from each side
y = x
The values are the same. Let's work them as all x, then.
Back to the first problem:
3x + 7x = -10
10x = -10
Divide each side by 10
x = -1
If x is -1, plugging it into the second equation...
4(-1) + 6y = -10
-4 + 6y = -10
Add 4 to each side
6y = -6
Divide each side by 6
y = -1
Both x and y = -1
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