what's up guys in this video I want to
go through a simple example of solving a
system of equations using substitution
of simultaneous equations
now the simple advice that I usually
give my students is whenever you have a
coefficient of 1 or negative 1 then you
want to use substitution now in this
example you could definitely use
elimination as well but I want to focus
on substitution because that's something
I'm going to be expanding upon on
further videos so the main thing we want
to do is like we have a lot of ones in
front of our X in front of our variables
we have one in front of this x one from
this X and one in front of a negative Y
and one question I get all the time from
students is like how do you know what is
going to be the easiest and here's the
way that I look at it I could solve for
x here but then I'm going to have to
subtract a 3y and you know I don't know
those are a little bit more numbers
whereas in here if I solve for x all I
got to do is add the Y and then what I'm
going to have is a 2 plus Y and to Me 2
plus Y is simpler than a 6 minus a3i it
could not be right when we actually get
into the math but the what I want to do
is just try to identify like what is
going to be this easiest way to solve
for something right it's going to be
easier to solve for x just by adding a y
rather than subtracting an X and then
dividing by negative one right that's
not going to make that really that
opinion feeling to be able to solve for
there so either it doesn't really matter
if you get confused maybe just like work
through it and just pick one but in this
example I'm going to go ahead and solve
for x in the top equation
okay now you could definitely write this
as a y plus two it doesn't really matter
ladies and gentlemen but the important
thing is now we've isolated a variable
we've solved for X okay and again you
could solve for y you could solve for x
in the bottom equation it doesn't matter
don't let that hold you back now what
we've done is we solved for X in this
top equation right now we're going to do
is we know the value of x is 2 plus y so
what I'm going to do is I'm going to
kind of put parentheses around this and
say all right if x is equal to 2 plus y
then in the second equation I can
replace this x with the parentheses 2
plus y
okay so now what I want you to be able
to understand is taking the top equation
and plugging into the second equation
I've now created this third equation
right if we're going to say like this
equation one this is equation two now
I've taken this third equation that only
has y's now I can combine my like terms
and now go ahead and solve for y
so we solve for y and this is a common
mistake that students will make is that
we're like all right I'm done like I
solve for the equation right we get so
happy when we've been able to solve an
equation that we kind of totally forget
what exactly we're trying to do when
we're looking at a system of equations
what we're trying to do is find the
values that are going to make these two
equations true for both X and Y because
you need to understand these are what we
call linear equations
and so if we were to graph linear
equations over here they you know I have
no idea what these graphs look like I'm
not trying to mimic them the important
thing I want you to understand is like
they could not they could be parallel
right where they don't intersect that
would be an example of having no
solution but when they do intersect
unless they're infinite many solutions
they're going to intersect at one point
right and that one point is going to
have an X as well as a y coordinate so
when we're looking at intersection lines
we're looking for that one X and Y so
right now we just solve for y right
we've got to go and find for X like
you're not solving the systems of
equations unless you solve for x as well
as for y so or A and B depending on
whatever your equation is so in this
example we have y is one now this so
such the cool thing about doing this
when you using substitution is we've
already set this equation equal to X so
if I know Y is now equal to one if I
want to solve for x all I simply need to
do now
is just go ahead and plug in A2 plus
what was y was was equal to a one so
therefore X is now equal to A3 so y
equals 1 x is equal to three and if you
wanted to use this as a coordinate point
then you can simply just write this as a
3 comma 1. Now overall this example was
easy and I did that for a reason but if
you want to be able to learn how to
solve simultaneous equations that are
not linear then go and check out the
next video I have for here
