Algebra 1 help » Equations / Inequalities » equipment of Equations » Equations / equipment Sets » just how to uncover the solution for a device of equations

A cube has a volume of

*
 
*
. If its width is 
*
 
*
, its length is 
*
*
, and also its height is 
*
 
*
, discover
*
.

You are watching: Finding the solution set of an equation


*


*


*


*


Explanation:

Since the thing in question is a cube, every of that sides must be the exact same length. Therefore, to acquire a volume of

*
 
*
, every side have to be equal to the cube source of
*
, i m sorry is
*
 cm.

We deserve to then collection each expression equal to

*
.

The first expression

*
 
*
 can be addressed by either
*
 or
*
, but the various other two expressions make it obvious that the equipment is
*
.


Explanation:

The most simple technique for addressing systems the equations is come transform one of the equations therefore it permits for the canceling the end of a variable. In this case, we deserve to multiply

*
 by
*
 to gain
*
.

 Then, we can include

*
come this equation to productivity
*
, for this reason
*
.

We can plug that value into either of the original equations; for example,

*
.

So,

*
 as well.


Explanation:

By fixing one equation because that

*
, and also replacing 
*
in the various other equation through that expression, you generate an equation of just 1 variable which have the right to be easily solved.


Explanation:

*

*

To settle this device of equations, use substitution. First, convert the second equation to isolate

*
.

*

Then, substitute 

*
right into the very first equation for
*
.

*

*

Combine terms and also solve for

*
.

*

*

Now the we understand the worth of

*
, we have the right to solve because that
*
utilizing our ahead substitution equation.

*


Explanation:

When we include the two equations, the 

*
and 
*
variables publication leaving united state with:

*
which method there is no equipment for this system.


Explanation:

First, combine like terms to obtain

*
. Then, subtract 12 and
*
from both sides to different the integers from the
*
"s to get
*
. Finally, division both sides by 3 to get
*
.


Explanation:

We are provided the complying with system the equations:

*

*

We are to find 

*
and also
*
. We can solve this through the substitution method. First, substitute the 2nd equation into the first equation to get

*

Solve for 

*
by adding 4x to both sides

*

*

Add 5 come both sides

*

*

Divide through 7

*

*

So

*
. Usage this value to find 
*
using among the equations native our provided system of equations. I think I"ll usage the an initial equation (can likewise use the 2nd equation).

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*

*

*

*

*

So the 2 linear functions intersect at

*


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