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Sumario sistemas de ecuaciones

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Sistemas de ecuaciones, resumen completo

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  • January 28, 2024
  • 4
  • 2023/2024
  • Summary
  • Secondary school
  • Bachillerato
  • 3
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Objetivo 3
!!!!..! !




1
resolver un sistema de ecuaciones lineales usando sustitución
ejer ricjof:
gemplo:
·




utilizar la sustitución para resolver sistema:

·Y
* el



X 11 2y
+
=

y 2X=
-
14



3x 35
+
6y
2(x zy) Sy
- =
-
+ =
- 23
① desperar
+


la variable
X= X 11=
2)
+ -
5)
Sy=
⑦ 22 2y 23
-
sustituir
+ +

= en la otra
y
X 11=
-
10
ecuación.
8y 5y 23 22
-

Explicación:
+
+ -
=
=


X 1
la primera ecuación indica
iguales

son
yy 2x-10
nos que


a?e
sustituir en la


y 2x
=
-
12
ecuación despe, ada





por lo tanto, podemos sustituiry por 2x-1 en la otra ecuacion.
y S
=

-




3x 5y 35
-
+ =
-




-
3x 5/2x 12)
+ -
=
-
35
3

*
a
y 3x 10
= +




luego, resolvemos para X

a e)
=
-
ex +


Sy 1t
= - -
3) Sy+
17
=


3x 5)2X 10) 35
=
-
+ - -


1t
Sy
5(yy 12
+


a) 3y
=


9 ex 5(3x 10) 17
=
+ + +
35
-
3x 10x
=
70
- - - +
+
=




17 12
Sy
-




3y
+
=



15y es
+

a
z)
+



3) ex 15X 50
=

7x - 70 =
- 35 5x + -
9
=
- +
+ 17
=




Sy S
=



15y 3y q +
=
- 05 ex 15X 1 7 =
50
5x
+
-
7x 35
-
6 9
=
=
-



y 1 =




1x
18y 36
=
-
X 5
=




y
- SYe
=




por último, sustituimos por X 5
=
en una de las ecuaciones

originales y recolvemos paray.
y = -2 5
-vamos a utilizar y 2x-10, porque y
=

ya estáaislado X 3 =




y 2x
=

-
12


y 2
=
(5) - 12



2
y
=
-




X 5
=




-(x 3y 8 38x
y
-
=
y
-
2 =
2
=




-



4x 61
+
=
-
70 -11X Iy
-
=
-
27
2x 6) x)
=
- +
- - 70

3y 12
11(2)
=
-
y 27
=
- -
-

3x 6
- =


2x -

21
=
-
20
-
-



2
metodo de suma y resta y = -
22 27
y
-
-
=



X 6
=




34
-




-2x 20 20
-3
=
-

-iemplo:Sx
+


2 y 2
y 27 22
-
= - +
+
- =




30 y
=
2
3x X 2
= - =
-
2y 2x 2 S
-


y =
- -
=




X 1
=




y -
=




0 -
2 -
I
x zy -
+ =




X =

2 y 5
- =



3x -
21 20
=




IY
&X 0y
+
16
=
↑ 2X 2x +

e(2) -
=
a


I
SX -2 y 11 X 2y 4
=
-
=




&X 2x
-


16 2x 8
17)
= +

8
=
-

(x Sy X 5y 17
- =
=
-
- +
- +



sustituir zy 18
1
8
=

x =

x 2x
=
- -
8
+17 7y 78
- =



Sy
=

x
-
-



y 1
=


2x
=
16
X I
=
5x zy +
=
=
c -



7 y 18
=



X

s
16
=
-




y 2 2( a)
=


t
-
11
-
=

x
-
-


2

X X
=


2y 12 8 8 11 =
= +

y 0
-
- =

-




y 7 x 11 8
=
= -
-




y
X 2
3
= =



=
7
y -




I
3 3x 2y 8
-

6 =

verbal que involucra
+



resolver un problema una suma yotra relacion
simple utilizando un sistema de ecuaciones lineales. 6x -


2y
=

- 20


pregunta
-




3x =
=
12
6x 20
=
-
zy
-

una clase de
geometria tiene un total de 82 estudiantes, el número de mujeres es o menos que el himero
x
12
=
=
de hombres. Scrantos hombres y cuantas mujeres están en la clase?
6 - 0)
zy 10
=
-
-
3
-
procedimiento
20
-



2y - 70
- =



x 2
=

-

X hombres
=




2y - 20 10
- = +



y mvieres
=




4
=




zy
-




O
convertir la informacion a ecuacion

la clase tiene 2 estudiantes y 1 =




&19 2
-




sumadez números:5 8
x y
=

& 2
+




y
=



=número
* más
-
2
grande: 1 2

el número de mujeres es o menos que el número de hombres y número
=
más pequeno:1 0
y x G
=
-




x y 56
② la
+ =



podemos sustituir y
X- s
=
en primera ecuación para hallar X


3y y 56
*,o
=
+




x y 4 2 la

=


sustituir X=ze primera
+

en
↑y 56
=




ecuación X = 4 2
x +
(x -
6) 02 =

para hallar y
y 12
=




x y 02
=
+

2x -
6
=
0 2


20 y 02
=

08
=

2x
+




X 20 y 18
= =

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