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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