SOLUTION: Hi, I need help on a linear equations word problem and when translating I got x+y=115, x+y=21, did I translate it right? Translate to a system of equations and solve: The sum o

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Hi, I need help on a linear equations word problem and when translating I got x+y=115, x+y=21, did I translate it right? Translate to a system of equations and solve: The sum o      Log On


   

Question 1158446: Hi, I need help on a linear equations word problem and when translating I got x+y=115, x+y=21, did I translate it right?
Translate to a system of equations and solve:
The sum of two numbers is 115. The difference is 21. Find the numbers.
Found 2 solutions by Boreal, MathLover1:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
difference means subtraction
x-y=21
then by adding
2x=136
x=68
y=47

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
x%2By=115..........eq.1
x%2By=21...........eq.2
Translate to a system of equations and solve:
The sum of two numbers is 115. ->correct
The difference is 21. ->incorrect=>x%2By=21 is also the sum of two numbers
x%2By=115..........eq.1
x%2By=21...........eq.2
----------------------------subtract eq.2 from eq.1
x%2By-%28x%2By%29=115-21
x%2By-x-y=94
0=94-> no solution exist (equations above represent two parallel lines)
+graph%28+600%2C+600%2C+-10%2C+125%2C+-10%2C+125%2C+115-x%2C21-x%29+


but, if you made mistake typing x%2By=21 and if it is acctualy difference, then you have
x-y=21...........eq.2
and system is

x%2By=115..........eq.1
x-y=21...........eq.2
----------------------------subtract eq.2 from eq.1
x%2By-%28x-y%29=115-21
x%2By-x%2By=94
2y=94
y=47
go to
x-y=21...........eq.2, plug in y value
x-47=21
x=21%2B47
x=68



check solution:

x%2By=115=>68%2B47=115=>115=115
x-y=2168-47=21=>21=21