Pregunta
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The solutions are
and
.
Solución
-
Solve the first equation for
: -
Substitute
into the second equation: -
Simplify the equation:Combine
terms: Combineterms: So the equation becomes: -
Multiply the entire equation by
to eliminate fractions: -
Solve the quadratic equation using the quadratic formula:Calculate the discriminant:Taking the square root:Thus:This gives two solutions:
-
Find
for each value of using : - For
: - For
:
- For
-
The solutions to the system are:
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Como
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Mind Expander
To solve the given system of equations, let’s begin with the first equation
. We can express
in terms of
as follows:
Now, let’s substitute this expression for
into the second equation:
Simplifying
:
Substituting this back into the equation, we get:
Combining like terms, we can rewrite
as
:
This simplifies to:
Writing
with a common denominator of 3 gives
:
Calculating
:
To eliminate the fractions, multiply through by 9:
Rearranging gives:
Now we can use the quadratic formula
:
Here,
,
, and
:
First, calculate the discriminant:
Now, apply the quadratic formula:
or
Now let’s find the corresponding
values:
For
:
For
:
Thus, the solutions to the system of equations are:

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