SOLUTION: Write a system of linear equations for the following problem: the sum of two number is 80. The smallest number is seventy less than two times the larger number. find the two number

Algebra ->  Linear-equations -> SOLUTION: Write a system of linear equations for the following problem: the sum of two number is 80. The smallest number is seventy less than two times the larger number. find the two number      Log On


   

Question 115827: Write a system of linear equations for the following problem: the sum of two number is 80. The smallest number is seventy less than two times the larger number. find the two numbers.
Found 2 solutions by checkley71, MathLover1:
Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
x+y=80 or x=80-y
x=2y-70 now replace x with(80-y) in the second equation:
80-y=2y-70
-3y=-150
y=-150/-3
y=50 answer.
x+50=80
x=80-50
x=30 answer.
proof
30=2*50-70
30+100-70
30=30

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
the sum of two number is 80:
Let numbers be x and y where x%3Cy, then we have

x%2By=80
The smallest number (x) is seventy less than two times the larger number (y)
x+%2B+70+=+2y
find the two numbers by solving this system
x%2By=80.........subtract (2) from (1)
x+%2B+70+=+2y………(2)
-------------------------------------
x-x%2By-70=80-2y
+y-70=80-2y………move -70 to the right and -2y to the left
+y+%2B+2y+=+80+%2B+70………
++3y+=+150………..divide both sides by 3
++3y%2F3+=+150%2F3………
++y+=+50………now find what x is equal to

x%2By=80…………(1)………plug in y value
x%2B50=80…………………move50to the right
x=80-50…………
x+=+30…………
So, your answer is:
x+=+30
++y+=+50