SOLUTION: the sum of two numbers is seven less than five times the smaller number. twice the larger number is one more than thrice the smaller number. find the numbers

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> SOLUTION: the sum of two numbers is seven less than five times the smaller number. twice the larger number is one more than thrice the smaller number. find the numbers       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1009471: the sum of two numbers is seven less than five times the smaller number. twice the larger number is one more than thrice the smaller number. find the numbers
Answer by Cromlix(4381) About Me  (Show Source):
You can put this solution on YOUR website!
Hi there.
the sum of two numbers is seven less
than five times the smaller number.
x + y = 5(x) - 7
x + y = 5x - 7
x - 5x + y = -7
-4x + y = -7........(1)
Twice the larger number is one more
than thrice the smaller number.
2(y) = 1 + 3(x)
2y = 1 + 3x
-3x + 2y = 1........(2)
...............
-4x + y = -7........(1)
-3x + 2y = 1........(2)
Multiply Eq(1) by -2
8x - 2y = 14........(1)
-3x + 2y = 1........(2)
Add Eqs(1) + (2)
5x .....= 15
x.......= 3
Substitute x = 3 into
Equation (1)
-4x + y = -7
-4(3) + y = -7
-12 + y = -7
y = -7 + 12
y = 5
Two numbers are: 3 and 5
Hope this helps :-)