the sum of two numbers is 19. three times the first number minues four times the second number is eight. find the two numbers

he sum of two numbers is 19. three times the first number minues four times the second number is eight. find the two numbers

OK...call the first number "x,' and the second number "y"

Then, x + y = 19

And three times the first (3x) plus four times the second (4y) = 8

Mathematically, we have

x + y = 19

3x - 4y  = 8

We can solve this by one of two methods (besides just guessing, of course !!) - either sustitution or elimination. I'll use the substitution method.

If I subtract the "x" from both sides in the first equation, I have y = 19 - x

So, in the second equation I can "substitute" "19 - x" for "y."

So we have

3x - 4(19-x) = 8    Note that this gives us an equation in one variable that should be easy to solve.  We have

3x - 76 + 4x = 8    And simplifying gives us

7x - 76 = 8

Add the "76" from both sides and we get

7x = 84   dividing both sides by 7   we have

x = 12  

Now...... knowing that y = 19 - x, I'll let you find  "y".