Algebra 1 assist » Equations / Inequalities » Systems of Equations » Equation / Equipment Setns » how to discover ns Systems for a mechanism that equation

A cuit is in has a volume the

 
*
. If itns width is 
 
, itns length is 
*
, and itns height is 
 
, discover
.

You are watching: Give a geometric description of the following systems of equations





*


Explanation:

Due to the fact that ns thing in Inquiry ins a cube, every that itns sides have to it is in ns very same length. Therefore, to gain a voluns the

 
, every side must it is in same come ns cube source that
, which ins
 cm.

us have the right to then set each expressitop top equal to

*
.

the first expressitop top

 
*
 deserve to be solved by eitshe
*
 or
*
, but the other 2 expressions make it obvious the the Equipment is
.


Explanation:

ns Many basic strategy for addressing Systems that equations is to transform among the equation for this reason ins allows for the canceling the end that a variable. In thins case, us have the right to main point

*
 by
*
 to get
.

 Then, we deserve to include

*
to thins equati~ above come productivity
*
, therefore
*
.

we can pluns that worth into eitshe the ns Original equations; because that example,

*
.

So,

 together well.


Explanation:

by addressing one equati~ above for

, and also replacing 
in the other equatitop top with that expression, girlfriend generate an equati~ above that only 1 change i beg your pardon deserve to be readily solved.


Explanation:

come deal with this mechanism the equations, use substitution. First, transform ns Second equatitop top come isoso late

.

*

Then, substitute 

*
into the first equati~ above because that
*
.

*

*

combine terms and deal with for

.

currently that us recognize ns worth of

*
, we can solve because that
making use of ours previouns substituti~ above equation.


Explanation:

once we add the 2 equations, the 

*
and 
*
variables cancetogether leaving us with:

*
which implies tright here is no Equipment because that this system.


Explanation:

First, combine choose terms come gain

. Then, substreet 12 and
indigenous both political parties come sepaprice the integerns indigenous ns
*
"s come acquire
. Finally, division both political parties by 3 to get
*
.


Explanation:

us are provided ns following mechanism of equations:

*

us are to find 

*
and
. Us can deal with this with the substitution method. First, substitute ns Second equatitop top right into the initially equati~ above to get

*

resolve for 

*
through including 4x to both sides

*

*

include 5 come both sides

division through 7

*

*

therefore

. Use this value to find 
*
using one of ns equations from our given system that equations. I think I"ll use ns initially equati~ above (have the right to additionally use the 2nd equation).

*

*

*

therefore ns two straight features crossing at


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