ShmoopTube
Where Monty Python meets your 10th grade teacher.
Search Thousands of Shmoop Videos
Math II Videos 98 videos
ACT Math Pre-Algebra: Drill 3, Problem 4. Find the solution to this equation.
Solving Systems of Equations by Substitution 14326 Views
Share It!
Description:
We just love us some alliteration.
Transcript
- 00:04
Solving Systems of Equations by Substitution a la Shmoop
- 00:08
After leaving his day job as a substitute teacher… [Man walking through a school corridor]
- 00:11
…Mister Uboat goes to his evening job as a substitute particle physicist. [Mr Uboat in a lab coat]
- 00:16
Today's task at the lab is simple... solve for x and y to correctly align the particle [Two cannons labelled x and y shoot cannonballs]
- 00:22
cannons.
Full Transcript
- 00:25
There are two equations, and x and y are the same value in each...
- 00:29
two-x minus three-y equals negative-two...
- 00:31
and...
- 00:32
four-x plus y equals twenty-four. [Equations written on a blackboard]
- 00:35
As a substitute, Mr. Uboat gets paid by the day, so he wants to get this done as efficiently [Flask bubbling]
- 00:39
as possible.
- 00:41
Let's solve this using, substitution.
- 00:45
The second equation looks easier to solve, so we'll start with that one. [The second equation lights up]
- 00:48
If we subtract four-x from both sides, we see that y equals twenty-four minus four-x.
- 00:54
Now we'll just substitute y for 24 minus 4x into the first equation...
- 00:59
to get two-x minus three, times open parenthesis, twenty-four minus four-x, closed parenthesis,
- 01:06
equals negative two. [The working written out on a blackboard]
- 01:09
Following the order of operations, we first distribute the minus 3 times the equation in the
- 01:14
parentheses.
- 01:15
Negative 3 times 24 equals 72, and negative 3 times negative 4x equals 12x, that's positive. [Finger pointing to the equation]
- 01:21
When we write it all out we get two-x minus seventy-two plus twelve-x equals negative
- 01:28
two.
- 01:29
Combining the x's together on the left side, we get fourteen-x minus seventy-two equals [The x's are highlighted]
- 01:34
negative-two.
- 01:36
Add seventy-two to both sides, and see that fourteen-x equals seventy.
- 01:40
Divide both sides by fourteen...and x equals five.
- 01:45
Now, remember how y equals twenty-four minus four-x?
- 01:50
Well, plug x as five into this equation to see what equals and you get twenty-four minus four times
- 01:58
five.
- 01:59
In other words, y equals twenty-four minus twenty, or y equals four. [Equation being solved on the blackboard]
- 02:06
Our answer is five, four.
- 02:08
Thanks to Mr. Uboat, the equation is solved!
- 02:11
Now the particle cannons can collide particles in peace. [The cannons fire and an explosion follows, Mr Uboat emerges with a black face and frazzled hair]
Related Videos
We don't like knocking people down to size, but we do like simplifying radicals. Join us?
If fleeing criminals always fled the scene of the crime at perfect right angles, it would be much easier to determine their whereabouts. Fortunatel...
Okay, so this probably isn't going to help you master Pokemon Go, but game theory can be applied to all sorts of situations. Even stomping your old...
Today's video is about calculating central tendency. We'll lay out outliers and make means...meaningful.