SOLUTION: The sum of two numbers is 29. Their difference is 7. What are the two numbers

Question 124692: The sum of two numbers is 29. Their difference is 7. What are the two numbers
Found 2 solutions by gems, jim_thompson5910:
Answer by gems(12) (Show Source): You can put this solution on YOUR website!
add the two equations
2x=36
divide both sides by 2
x=18
if x = 18, substitute in the 1st equation x+y=29
18+y=29
y=29-18
y=11
therefore x=18, y=11

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
The sentence "The sum of two numbers is 29" translates to the equation

The sentence "Their difference is 7" translates to the equation

Start with the given system of equations:

Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.

So let's isolate y in the first equation

Start with the first equation

Subtract from both sides

Rearrange the equation

Divide both sides by

Break up the fraction

Reduce

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

Since , we can now replace each in the second equation with to solve for

Plug in into the first equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.

Distribute the negative

Combine like terms on the left side

Add 29 to both sides

Combine like terms on the right side

Divide both sides by 2 to isolate x

Divide

-----------------First Answer------------------------------

So the first part of our answer is:

Since we know that we can plug it into the equation (remember we previously solved for in the first equation).

Start with the equation where was previously isolated.

Plug in

Multiply

Combine like terms

-----------------Second Answer------------------------------

So the second part of our answer is:

-----------------Summary------------------------------

So our answers are:

and

which form the point

So the two numbers are 18 and 11
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