SOLUTION: The sum of two numbers is 6 less than twice the first number. Their difference is 10 less than four times the second number. Find each of the numbers.

Question 546986: The sum of two numbers is 6 less than twice the first number. Their difference is 10 less than four times the second number. Find each of the numbers.
Answer by Maths68(1474) (Show Source): You can put this solution on YOUR website!
Find each of the numbers.
Let
First Number = x
Second Number = y
Given
The sum of two numbers is 6 less than twice the first number.
x+y=2x-6
x-2x=-y-6
-x=-y-6
Multiply by -1 both sides
(-1)(-x)=(-1)(-y-6)
x=y+6
x-y=6..................(1)

Their difference is 10 less than four times the second number.
x-y=4y-10
x-y-4y=-10
x-5y=-10...............(2)
Subtract (2) from (1)
x-5y=-10
-x+y=-6
-------------
-4y=-16
-4y/-4=-16/-4
y=4
Put the value of y in (1)
x-y=6..................(1)
x-4=6
x=6+4
x=10

First Number = x = 10
Second Number = y = 4

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