Hey there I have an awesome lesson for you today because today I am showing you how to solve systems of equations
using the substitution method
Today's lesson is part two
two in a three-part series on solving systems of equations
So if you are brand-new to systems of equations
I recommend you go watch part 1 first where I introduce what systems of equations are and if you've already watched that
You're ready for part two where we solve them using the substitution method. Let's get started
Whenever you are given a system of equations and asked to solve what that really means is that you have two or more
Equations and you need to find the intersection
point or points and the most common case you're going to run into is
Being given two linear equations and looking for their intersection point now there are three
Possible scenarios you can have with a system of linear equations most often
They are going to intersect in one point
although if they are parallel lines
They will never intersect and if they are really the same line
Then they are going to intersect in infinitely many points
If you'd like a recap of those scenarios and exactly what that looks like check out my tutorial on
systems of equations the graphing method
so today we are looking at the substitution method and in that method we want to
isolate a variable in one of these equations and then substitute that
Relationship into the other equation to begin with you always want to scan your equations and see if there's any nice
Variables to work with so if you see a variable that doesn't have a number coefficient written written in front
It is most likely the easiest
Variable to isolate. So in problem number one here. We have 2x plus y equals one and 3x plus 4y equals 14
I notice immediately that the Y in the first equation doesn't have a coefficient written in front of it
So that is the variable I want to isolate
After solving for y I get y equals 1 minus 2x
And now what I want to do here is take this relationship and substitute it in for y and the other equation
With that will give me is an equation
That only has X variables and once I have an equation with one variable I can solve for that variable
So here I have replaced Y in this equation
with what Y is equivalent to which is 1 minus 2x and
Now I have an equation with only X's in and my next step here is to solve for X
So I'm going to begin by distributing 4 through and then combining like terms and solving
Now that I know what X is I can go ahead and plug it back into this equation here to find y
Now we have discovered the X&Y
Coordinate where these two lines intersect and I'm just going to write my final answer as a coordinate point
In this second problem
I have negative 7x minus 2y equals negative 13 and X minus 2ax equals 11
So if I'm going to use the substitution method the easiest variable to isolate in this problem will be this X in the second equation
So my first step is to take this second equation and rearrange it so X is alone
Now that I have what X is equivalent to I can go ahead and plug it in for X in the other equation
So here I just replaced X with my equivalent relation, which is 2y plus 11 and notice here how when I
substituted this
Relationship in for X I made sure to put parentheses and that's a really important step
Because that ensures that this negative 7 is going to be distributed to both terms
Next I am going to distribute the negative 7 through combine like terms and solve for y
So here I get y equals negative four
and once again
my last step is to take that negative four and plug it back in for y the easiest place to plug it in is the
Relationship we have here where X is isolated. So I'm going to replace Y in the 2y plus 11 with negative 4
Okay, now I have my XY coordinate pair and of course the last step is to write that as an XY coordinate
So the place where these two lines intersect is at the coordinate point 3 negative 4
So in this final problem
We are going to approach it just like we did in the last two problems
now the only difference between this problem and the previous problems is that the numbers aren't quite as friendly there is
No variable that is lacking a coefficient like we had in the first two examples
so I'm just going to pick whichever variable I want to solve for and
I'm gonna make my decision based off of what looks like it will be the easiest
So in equation one, it's they're all multiples of two
So I think that those numbers will reduce a little bit easier than having numbers that aren't so compatible like in the second equation
And I'm just going to do that just because I want to avoid any fractions. Sometimes it's unavoidable
But here I think we can get around it
So I'm going to take the first equation and I could solve for either X or Y
And I think I'm going to solve for x
Okay there I have found my
relationship now that I know that X is equivalent to 3 y minus 3
I'm going to go ahead and replace X in the other equation
with 3 y minus 3
I have found that y equals two
And once again, my final step is to take that value and plug it into
This equation for y
And now that I know what x and y is just going to write the coordinate point
Next time on Math Hacks I'm going to show you how to use the elimination method to solve systems of equations
so you're gonna want to make sure to subscribe to the channel to get updates on that and
Why don't you increase your math karma today by giving this video a big thumbs up to recommend?
Until next time I'm Brett and thank you so much for joining me
