SOLUTION: The sum of two numbers is 22 when the larger number is subtracted from three times the smaller the difference is 6 what are the two numbers

Question 202006: The sum of two numbers is 22 when the larger number is subtracted from three times the smaller the difference is 6 what are the two numbers
Found 2 solutions by jim_thompson5910, RAY100:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
"The sum of two numbers is 22" translates to

"the larger number is subtracted from three times the smaller the difference is 6" translates to

Start with the given system of equations:

Add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:

Group like terms.

Combine like terms.

Simplify.

Divide both sides by to isolate .

Reduce.

------------------------------------------------------------------

Now go back to the first equation.

Plug in .

Multiply.

Subtract from both sides.

Combine like terms on the right side.

So the solutions are and .

So the larger number is 15 and the smaller number is 7.
Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
(1) x+y=22
(2) 3x -y =6,,,,,,,x = smaller,,,y=larger
.
from (1) y=22-x
.
subst into (2),,,3x -(22-x) = 6
3x -22+x = 6
4x = 22+6=28
x=7.
.
y=22-x = 22-7 = 15
.
check,,,, (1) 7 + 15 = 22,,,,,ok
(2) 3(7) - 15 = 6,,,,,ok

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