You can
put this solution on YOUR website!Let x=1st # and y=2nd #
Translate the following:
"The difference of two numbers is 86" becomes
"The second is 6 less than 5 times the first" becomes
Start with the given system
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
Subtract 6 from both sides
Combine like terms on the right side
Divide both sides by -4 to isolate x
Divide
Now that we know that
, we can plug this into
to find
Substitute
for each
Simplify
So our answer is
and
You can
put this solution on YOUR website!With the information which we have been given, we can set up equations to solve for the variables.
The difference of the two numbers is 86:
-x + y = 86
The second is 6 less than 5 times the first:
y = 5x - 6
we can put these together as a system:
-x + y = 86
5x - y = 6
By using the elimination method, we have
4x = 92
x = 23
Now using the method of substitution, we can plug 23 into one of the equations to find y.
-(23) + y = 86
y = 109
We can check our answer by plugging both values in for x and y.
-(23) + (109) = 86
86 = 86
5(23) - (109) = 6
6 = 6
Both of these statements are true,
x = 23
y = 109
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