Question 120139
Let x = the larger number
Let y = the smaller number
:
Write an equation for what it says:
:
"Twice the larger of the two numbers is three more than five times the smaller,"
2x = 3 + 5y
Or
2x - 5y = 3
:
"and then the sum of four times the larger and three times the smaller is 71."
4x + 3y = 71
:
What are the nos.? 
:
Multiply 2x+3y=3, by 2, and subtract 4x+3y=71 from it
4x - 10y = 6
4x +  3y = 71
--------------- subtracting eliminate x; find y
0x - 13y = -65
y = {{{(-65)/(-13)}}}
y = +5
:
Find x using the 1st equation
2x = 3 + 5(5)
2x = 3 + 25
2x = 28
x = 14
The two numbers are 14 and 5
:
Check solution in the statement:
the sum of four times the larger and three times the smaller is 71. 
4(14) + 3(5) = 71