SOLUTION: the difference between seven times one number and three times a second number is 25. The sum of twice the first and five times the second is 95. Find the numbers.

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Question 494308: the difference between seven times one number and three times a second number is 25. The sum of twice the first and five times the second is 95. Find the numbers.
Answer by Maths68(1474) About Me  (Show Source):
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Let x and y are two numbers
According to given conditions
7x-3y=25 ………..(1)
2x+5y=95……..(2)
Multiply (1) by 2 and (2) by -7 and add
14x-6y=50
-14x-35y=-665
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-41y=-615
y=-615/-41
y=15
Put the value of y in either equations (1) or (2) to get x
2x+5y=95……..(2)
2x+5(15)=95
2x+75=95
2x=95-75
2x=20
x=20/2
x=10
Numbers are 10 and 15
Check
Put the value of x and y in either equations (1) or (2)
7x-3y=25………..(1)
7(10)-3(15)=25
70-45=25
25=25