Solving Systems of Equations by Substitution
We just love us some alliteration.
|Algebra||Solve systems of equations|
Systems of Equations
There are two equations, and x and y are the same value in each...
two-x minus three-y equals negative-two...
four-x plus y equals twenty-four. [Equations written on a blackboard]
As a substitute, Mr. Uboat gets paid by the day, so he wants to get this done as efficiently [Flask bubbling]
Let's solve this using, substitution.
The second equation looks easier to solve, so we'll start with that one. [The second equation lights up]
If we subtract four-x from both sides, we see that y equals twenty-four minus four-x.
Now we'll just substitute y for 24 minus 4x into the first equation...
to get two-x minus three, times open parenthesis, twenty-four minus four-x, closed parenthesis,
equals negative two. [The working written out on a blackboard]
Following the order of operations, we first distribute the minus 3 times the equation in the
Negative 3 times 24 equals 72, and negative 3 times negative 4x equals 12x, that's positive. [Finger pointing to the equation]
When we write it all out we get two-x minus seventy-two plus twelve-x equals negative
Combining the x's together on the left side, we get fourteen-x minus seventy-two equals [The x's are highlighted]
Add seventy-two to both sides, and see that fourteen-x equals seventy.
Divide both sides by fourteen...and x equals five.
Now, remember how y equals twenty-four minus four-x?
Well, plug x as five into this equation to see what equals and you get twenty-four minus four times
In other words, y equals twenty-four minus twenty, or y equals four. [Equation being solved on the blackboard]
Our answer is five, four.
Thanks to Mr. Uboat, the equation is solved!
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]