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Example Questions
Example Question #1 : How To Find The Solution For A System Of Equations
A cube has a volume of
. If its width is
, its length is
, and its height is
, find
.
Since the object in question is a cube, each of its sides must be the same length. Therefore, to get a volume of
, each side must be equal to the cube root of
, which is
cm.
We can then set each expression equal to .
The first expression
can be solved by either
or
, but the other two expressions make it evident that the solution is
.
Example Question #1 : How To Find The Solution For A System Of Equations
Solve the system for and
.
The most simple method for solving systems of equations is to transform one of the equations so it allows for the canceling out of a variable. In this case, we can multiply by
to get
.
Then, we can add to this equation to yield
, so
.
We can plug that value into either of the original equations; for example, .
So, as well.
Example Question #2 : How To Find The Solution For A System Of Equations
What is the solution to the following system of equations:
By solving one equation for , and replacing
in the other equation with that expression, you generate an equation of only 1 variable which can be readily solved.
Example Question #1 : How To Find The Solution For A System Of Equations
Solve this system of equations for :
None of the other choices are correct.
Multiply the bottom equation by 5, then add to the top equation:
Example Question #2 : How To Find The Solution For A System Of Equations
Solve this system of equations for :
None of the other choices are correct.
Multiply the top equation by :
Now add:
Example Question #3 : How To Find The Solution For A System Of Equations
Solve this system of equations for :
None of the other choices are correct.
Multiply the top equation by :
Now add:
Example Question #4 : How To Find The Solution For A System Of Equations
Find the solution to the following system of equations.
To solve this system of equations, use substitution. First, convert the second equation to isolate .
Then, substitute into the first equation for
.
Combine terms and solve for .
Now that we know the value of , we can solve for
using our previous substitution equation.
Example Question #1 : How To Find The Solution For A System Of Equations
Find a solution for the following system of equations:
infinitely many solutions
no solution
no solution
When we add the two equations, the and
variables cancel leaving us with:
which means there is no solution for this system.
Example Question #9 : How To Find The Solution For A System Of Equations
Solve for :
None of the other answers
First, combine like terms to get . Then, subtract 12 and
from both sides to separate the integers from the
's to get
. Finally, divide both sides by 3 to get
.
Example Question #6 : How To Find The Solution For A System Of Equations
We have two linear functions:
Find the coordinate at which they intersect.
none of these
We are given the following system of equations:
We are to find and
. We can solve this through the substitution method. First, substitute the second equation into the first equation to get
Solve for by adding 4x to both sides
Add 5 to both sides
Divide by 7
So . Use this value to find
using one of the equations from our given system of equations. I think I'll use the first equation (can also use the second equation).
So the two linear functions intersect at
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