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

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

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

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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