SOLUTION: the difference between two numbers is -38. two times the smaller number minus five times the larger number is -217. what are the numbers?

Question 139168: the difference between two numbers is -38. two times the smaller number minus five times the larger number is -217. what are the numbers?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
the difference between two numbers is -38. two times the smaller number minus five times the larger number is -217. what are the numbers?
:
Let x = a number
Let y = another number
;
Write an equation for each statement:
"the difference between two numbers is -38."
x - y = -38
or
x = (y-38)
:
" two times the smaller number minus five times the larger number is -217."
2x - 5y = -217
:
what are the numbers?
:
Substitute (y-38) for x in the above equation, find y:
2(y-38) - 5y = -217
2y - 76 - 5y = -217
2y - 5y = -217 + 76
-3y = -141
y =
y = +47
:
Find x:
x = 47 - 38
x = +9
:
Check solutions in the statement:
"two times the smaller number minus five times the larger number is -217."
2(9) - 5(47) =
18 - 235 = -217; confirms our solutions
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