Sistema de ecuaciones lineales con dos variables
14
SISTEMA DE ECUACIONE S ALUMNA: Ramon Aguirre, Shania GRADO Y SECCION: 5to D
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Transcript of Sistema de ecuaciones lineales con dos variables
SISTEMA DE
ECUACIONESALUMNA: Ramon Aguirre, ShaniaGRADO Y SECCION: 5to D
1. 2x + 3y = 123x + 2y = 13
POR 3:6x + 9x = 36
POR -2:-6x + 4y = -26
6x + 9y = 13-6x + 4y = -26 5y = 10 y = 2
x y 3 2
0 4
x y 3 2
0 5
. ... 3x + 2y = 13
2x + 3y = 12
6x + 9(2) = 366x + 18 = 366x = 18X = 3
2. 5x – y = 73x + 2y = 12
5x – y = 75x= 7 + yX = 7 + y 5
3x + 2y = 123x = 12 – 2yx = 12 – 2y 3
7 + y = 12 – 2y 5 33(7 + y) = 5(12 – 2y)21 + 3y = 60 – 10y10y + 3y = 60 – 2113y = 39y = 39 13 y = 3
5x – y = 75x = 7 + (3)5x = 10X = 2
3x + 2y = 123x + 2(3) = 123x = 12 – 63x = 6X = 2
x y 2 3
0 - 7
x y 2 3
0 6
.
... 5x – y = 7
3x + 2y = 12
3. 3x + y = 5x – 2y = 11
y = 5 – 3x y = x – 11/2
5 – 3x = x – 11/210 – 6x = x – 1110 + 11 = 7x21 = 7x3 = x
x y 3 -4
0 5
x y 3 -4
0 -5
.
.. .X – 2y = 11
3x + y = 5
3(3) + y = 59 + y = 5Y = 5 – 9Y = -4
4. 2x + 3y = 35x – 6y = 3
2x + 3y = 32x = 3 – 3yX = 3 – 3y 2
5x – 6y = 35x = 3 + 6yx = 3 + 6y 5
3 – 3y = 3 + 6y 2 55(3 – 3y) = 2(3 + 6y)15 – 15y = 6 + 12y15 - 6 = 12y + 15y9 = 27y 9 = y27 y = 1
3
2x + 3y = 32x = 3 – 3(1/3)2x = 3 - 12x = 2X = 1
5x – 6y = 35x - 6(1/3) = 35x – 2 = 35x = 3 + 2X = 1
x y 1 1/3
0 1
x y 1 1/3
0 -1/2
.... 5x – 6y = 3
2x + 3y = 3
5. x/2 + 3y = 1X + 2y = 1
POR 2:X + 6y = 2
POR -3:-3x – 6y = -3
x + 6y = 2-3x – 6y = -3-2x = -1X = -1/-2X = 1/2
x y 1/2 1/4
0 1/3
x y1/2 1/4
0 1/2
. ..x/2 + 3y = 1 X + 2y = 1
1/2 + 2y = 1 2y = 1 – 1/2 2y = 1/2 Y = 1/2 y = 1/4
.
6. 1/x + 1/y = 53/x + 2/y = 12
POR 2:-2/x + 2/y = -10 3/x + 2/y = 12
-2/x + 2/y = -10 3/x + 2/y = 12-2/x + 3/2 = 2 1/x = 2 1 = 2x 1/2 = x
x y 1/2 1/3
0 1/5
x y 1/2 1/3
0 1/6
...
.1/x + 1/y
3/x + 2/y = 12 1/1 + 1/y = 51/2 2 + 1/2 = 5 1/y = 3 3y = 1 Y = 1/3
7. 5x/2 + 3y = 13x/2 – 3y = 15
5x/2 + 3y = 1 3x/2 – 3y = 155x/2 + 3x/2 = 16 8x = 32 X = 4
x y 4 -3
0 1/3
x y 4 -3
0 -5
.
.
..3x/2 – 3y = 15
5x/2 + 3y = 1
5(4)/2 + 3y = 1 20/2 + 3y =1 10 + 3y = 1 3y = -9 y = -3
8. 2(x-y) + (x – y)/3 = 3x - 1X – y = 3
2(x – y) + (x – y)/3 = 3x – 1 2(3) + (3)/3 = 3x – 1 6 + 1 = 3x – 1 7 = 3x – 1 8 = 3x 8/3 = x .
.
..
X – y = 3
2(x-y) + (x – y)/3 = 3x – 1
x – y = 38/3 – y = 3-1/3 = y
9. (8x – 3y)/4 = -93y = 12
8x – 3(4) = -9 48x – 12 = -9 48x – 12 = -368x = -24X = -3
.... 3x = 12
(8x – 3y)/4 = -9
Y = 4
x y -3 4
0 12
x y -3 4
0 4
10. (2x - y)/5 = x - 13x – (2x – y)/5 = 5
3x – (2x – y) = 5 53x – (x – 1) = 53x – x + 1 = 52x = 4X = 4/2X = 2 . .
.
. 3x – (2x – y)/5 = 5
(2x - y)/5 = x – 1
x y 2 -1
0 3
x y 2 -1
0 -25
2(2) – y = (2) – 1 54 – y = 1 54 – y = 5-y = 1Y = -1
(0;-25)
11. y = 4x/3 + 3y = 2x/3 + 7/3
4x + 3 = 2x + 7 3 1 3 34x + 9 = 2x + 7 3 3 4x + 9 = 2x + 72x = -2x = -1
x y -1 5/3
0 3
x y -1 5/3
0 7/3
....Y = 4x/3 + 3
Y = 2x/3 + 7/3
12. x/2 + 2y/3 = 1/2 5x/4 + 2y/3 = 3/4
POR -1:-x/2 – 2y/3 = 1/2
x y 5/3 -1/2
0 3/4
x y 5/3 -1/2
0 9/8
.... x/2 + 2y/3 = 1/2
5x/4 + 2y/3 = 3/4
-x/2 – 2y/3 = 1/25x/4 + 2y/3 = 3/4 -x/2 + 5x/4 = 1/2+ 3/4-2x + 5x/4 = 2 + 3/4 3x = 5X = 5/3
5/3 + 2y/3 = 1/2 25/6 + 2y/3 = 1/25 + 4y = 1 6 25 + 4y = 3Y = -1/2
13. 4x + 3(y – 1) = 53(y – 1) = 2x - 7
Y – 1 = 2x – 7 3
x y 2 0
0 8/3
x y 2 0
0 -4/3
. ...4x + 3(y – 1) = 5
3(y – 1) = 2x – 7
4x + 3(2x – 7) = 5 3 4x + 2x – 7 = 5 6x = 12 X = 2
4(2) + 3(y – 1) = 5 8 + 3y – 3 = 5 3y = 0 Y = 0
