Lesson notes
- You cannot solve one equation in two variables uniquely. You must express one variable in terms of the other variable using a second equation.
- For example, if I say sum of two numbers
and
is 150, I could form the equation
. But, I can have many possible values for
and
that satisfy this equation. For example,
is one possibility, but
is another possibility as well. And,
is yet another possibility. To find the precise values of
and
, you need to have the equation in terms of one variable only. If we have additional information such as
is twice
, we can form another equation
, and replace
in the first equation by
.
- When you replace one variable by another variable, be sure to use parenthesis. Remember, PEMDAS rules!
- For example, if I have an equation that says
, I cannot solve it to get exact values of
and
. I need to have an equation in only one variable. Now, if I have a second equation that says
, I can replace
in the first equation by
. Now, if I rewrite the first equation as
, this is wrong! Remember, in
,
is multiplied by
. So, we should have the whole of
to be multiplied by
. Thus, the correct way to write is using parentheses:
.
Equations in one variable
Exercises
Problem set
Solve for the variable in the following.
Problem set
Solve for the variable in the following.
Problem set
Solve for the variable in the following.
Problem set
Solve for the variable in the following.
Problem set
Solve for the variable in the following.
Problem set
Solve for the variable in the following.
Problem set
Solve for the variable in the following.
Problem set
Solve for the variable in the following.
Problem set
Solve for the variable in the following.
Problem set
Solve for the variable in the following.
Problem set
Solve for the variable in the following.
Problem set
Solve for the variable in the following.
Problem set
Solve for the variable in the following.
Equations in two variables
Exercises
Problem set
Solve for both the variables in each of the following.
and
and
and
and
and
Problem set
Solve for both the variables in each of the following.
and
and
and
and
and
and
Problem set
Solve for both the variables in each of the following.
and