Problemas
3. Construct Arguments Kavi solved the system of equations as shown. What mistake did Kavi make? What is the correct solution? 3x+4y=33 2x+y=17 y=17-2x 2x+(17-2x)=17 2x+17-2x=17 2x-2x+17=17 17=17 Infinitely many solutions
Roztwór
Vladimir
professionell · Tutor durante 6 años
4.3
(265 Votos)
Respuesta
To determine the mistake Kavi made and find the correct solution, let's analyze the steps Kavi took to solve the system of equations.Given system of equations:
Kavi's solution:
Kavi's mistake:Kavi correctly substituted the expression for
from the second equation into the first equation. However, he made an error in simplifying the equation. Specifically, he incorrectly simplified
to
, which is not correct.Correct solution:To solve the system of equations correctly, we can use the substitution method again. From the second equation, we have
. Substituting this expression for
into the first equation, we get:
Expanding and simplifying:
Now, substitute
back into the second equation to find
:
Therefore, the correct solution to the system of equations is
and
.