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Substitution Method - Algebra, Mathematics Video Lecture
FAQs on Substitution Method - Algebra, Mathematics Video Lecture
| 1. What is the substitution method in algebra? |  |
Ans. The substitution method is a technique used in algebra to solve a system of equations by replacing one variable with an expression involving the other variable. This method involves solving one equation for one variable and then substituting that expression into the other equation.
| 2. How does the substitution method work? | |
Ans. The substitution method works by solving one equation for one variable and then substituting that expression into the other equation. This allows us to eliminate one variable and solve for the remaining variable. By substituting the expression, we can simplify the equations and solve for the values of the variables.
| 3. When is the substitution method used in algebra? | |
Ans. The substitution method is used in algebra when we have a system of two equations with two variables. This method is particularly useful when one equation is already solved for one variable and we can easily substitute the expression into the other equation. It helps in finding the values of the variables that satisfy both equations simultaneously.
| 4. What are the advantages of using the substitution method? | |
Ans. The advantages of using the substitution method in algebra include its simplicity and flexibility. It allows us to solve a system of equations step by step, making it easier to understand the solution process. Additionally, it can be applied to a variety of equations and is suitable for both linear and nonlinear systems.
| 5. Are there any limitations or drawbacks of the substitution method? | |
Ans. While the substitution method is a powerful tool in solving systems of equations, it may not always be the most efficient method. In some cases, the equations may involve complex expressions or multiple variables, making substitution cumbersome. Additionally, the method may not work if the equations are inconsistent or have infinitely many solutions. In such cases, other methods like elimination or graphing may be more suitable.
Text Transcript from Video
use substitution to solve for x and y
and we have two equations two y is equal
to X plus seven and then we have X is
equal to Y minus four so let me just
rewrite this so this top equation is 2y
is equal to X plus seven and then this
bottom equation right over here they
tell us that X is equal to Y minus four
they say that X is equal to Y minus four
and so they give us what X is equal to
in the second equation so we can use
this information to substitute for X
right up over here if we want a solution
to both of these we just have to say
well look if 2y is equal to X plus seven
and we have the constraint X is y minus
four then everywhere where we see X in
this top equation we can substitute it
with Y minus four so I can rewrite this
top equation as as 2y is equal to
instead of writing X I can write Y minus
four Y minus four plus seven now this
equation right over here it's one
equation with one unknown it
incorporates information from both of
these it has both of these constraints
in it because I did the substitution for
X and now we can solve for the Y that
will satisfy both of these equations so
we get let's see if we simplify it we
get 2y is equal to Y minus four plus
seven that's y plus three we can
subtract Y from both sides and then we
get 2y minus y is y these cancel out and
you get Y is equal to three and then you
can take the three and put it back into
either one of these equations to solve
for X so we could do it right over here
in magenta X is equal to Y minus four we
know that Y is going to be equal to
three is going to is equal to three
minus four which is equal to negative
one so X is equal to negative one and
the solution that we got via
substitution is X is equal to negative
one and Y is equal to three if we want
to write it down
as an ordered pair and now we can go
back and check that this indeed is a
solution to both of these equations so
let's go to this top equation if you
have two times three we're saying Y is 3
when X is negative one should be equal
to negative one plus seven negative one
plus seven plus seven and this right
over here is six negative one plus seven
is six it definitely works for this top
equation and let me just be clear right
over here this negative one this
negative one is that negative one right
over there and that three is that three
but when you take X is equal to negative
one y is equal to three substitute in
this top equation it definitely works
now let's try the second one
so X is negative one X is negative one
negative one should be equal to Y minus
three it should be equal to three minus
four and we really already went through
this when we did it when we did this
when we took Y equaled three and we
solved for X but we'll just do it again
negative one is indeed three minus 4/3
minus four is negative one so it
definitely works in both of these
equations
and we have two equations two y is equal
to X plus seven and then we have X is
equal to Y minus four so let me just
rewrite this so this top equation is 2y
is equal to X plus seven and then this
bottom equation right over here they
tell us that X is equal to Y minus four
they say that X is equal to Y minus four
and so they give us what X is equal to
in the second equation so we can use
this information to substitute for X
right up over here if we want a solution
to both of these we just have to say
well look if 2y is equal to X plus seven
and we have the constraint X is y minus
four then everywhere where we see X in
this top equation we can substitute it
with Y minus four so I can rewrite this
top equation as as 2y is equal to
instead of writing X I can write Y minus
four Y minus four plus seven now this
equation right over here it's one
equation with one unknown it
incorporates information from both of
these it has both of these constraints
in it because I did the substitution for
X and now we can solve for the Y that
will satisfy both of these equations so
we get let's see if we simplify it we
get 2y is equal to Y minus four plus
seven that's y plus three we can
subtract Y from both sides and then we
get 2y minus y is y these cancel out and
you get Y is equal to three and then you
can take the three and put it back into
either one of these equations to solve
for X so we could do it right over here
in magenta X is equal to Y minus four we
know that Y is going to be equal to
three is going to is equal to three
minus four which is equal to negative
one so X is equal to negative one and
the solution that we got via
substitution is X is equal to negative
one and Y is equal to three if we want
to write it down
as an ordered pair and now we can go
back and check that this indeed is a
solution to both of these equations so
let's go to this top equation if you
have two times three we're saying Y is 3
when X is negative one should be equal
to negative one plus seven negative one
plus seven plus seven and this right
over here is six negative one plus seven
is six it definitely works for this top
equation and let me just be clear right
over here this negative one this
negative one is that negative one right
over there and that three is that three
but when you take X is equal to negative
one y is equal to three substitute in
this top equation it definitely works
now let's try the second one
so X is negative one X is negative one
negative one should be equal to Y minus
three it should be equal to three minus
four and we really already went through
this when we did it when we did this
when we took Y equaled three and we
solved for X but we'll just do it again
negative one is indeed three minus 4/3
minus four is negative one so it
definitely works in both of these
equations
About this Video
Oct 18, 2025
Last updated
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