Ayuda !!! D: 95 puntos
1) Resolver los siguientes sistemas por el metodo de igualacion
a)![\left \{ {{-7x-4y=-7} \atop {2x-y=2}} \right. \left \{ {{-7x-4y=-7} \atop {2x-y=2}} \right.](https://tex.z-dn.net/?f=%5Cleft+%5C%7B+%7B%7B-7x-4y%3D-7%7D+%5Catop+%7B2x-y%3D2%7D%7D+%5Cright.)
b)![\left \{ {{2y=7-x} \atop {2y=-6x-8}} \right. \left \{ {{2y=7-x} \atop {2y=-6x-8}} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7B2y%3D7-x%7D+%5Catop+%7B2y%3D-6x-8%7D%7D+%5Cright.+)
2) Resuelve los siguientes sistemas por el metodo de reduccion
a)![\left \{ {{2x+3y=1} \atop {x+y=-2}} \right. \left \{ {{2x+3y=1} \atop {x+y=-2}} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7B2x%2B3y%3D1%7D+%5Catop+%7Bx%2By%3D-2%7D%7D+%5Cright.+)
b)![\left \{ {{4y=3+x} \atop {10=3x+7y}} \right. \left \{ {{4y=3+x} \atop {10=3x+7y}} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7B4y%3D3%2Bx%7D+%5Catop+%7B10%3D3x%2B7y%7D%7D+%5Cright.+)
Por favor...
Respuestas
Respuesta dada por:
47
-7x-4y=-7
2x-y=2
se despeja la misma variable,en ambas ecuaciones y despues se iguala
-7x-4y=-7....-7x=4y-7......x=4y-7
-7
2x-y=2........2x=-y+2......x=-y+2
2
4y-7 =-y+2 ......2(4y-7)=-7(-y+2)....8y-14=7y-14....8y-7y=-14+14....y=0
-7 2
si y=0.......2x-y=2.....2x-0=2....2x=2.....x=2/2.....x=1
respuesta x=1 y=0
............................................................
2y=7-x............y=-x+7
2
2y=-6x-8........y=-6x-8
2
-x+7 =-6x-8 ......2(-x+7)=2(-6x-8).....-2x+14=-12x-16...-2x+12x=-16-14
2 2
10x=-30.......x=-30/10.......x= -3
si x= -3........2y=7-x.......2y=7-(-3)......2y=7+3.....2y=10.....y=10/2....y=5
respuesta x= -3 y=5
.................................................................
2x+3y=1
x+y=-2
1(2x+3y=1)...........2x+3y=1
-2(x+y=-2)............-2x-2y=4
y=5
si y=5.....x+y=-2......x+5=-2......x=-2-5........x=-7
respuesta x= -7 y=5
....................................................
4y=3+x....................-x+4y=3
3x+7y=10.................3x+7y=10
3(-x+4y=3).........-3x+12y=9
1(3x+7y=10)........3x+7y=10
19y=19.....y=19/19......y=1
si y=1......4y=3+x.......4(1)=3+x.....4=3+x......4-3=x.......1=x
respuesta x=1 y=1
2x-y=2
se despeja la misma variable,en ambas ecuaciones y despues se iguala
-7x-4y=-7....-7x=4y-7......x=4y-7
-7
2x-y=2........2x=-y+2......x=-y+2
2
4y-7 =-y+2 ......2(4y-7)=-7(-y+2)....8y-14=7y-14....8y-7y=-14+14....y=0
-7 2
si y=0.......2x-y=2.....2x-0=2....2x=2.....x=2/2.....x=1
respuesta x=1 y=0
............................................................
2y=7-x............y=-x+7
2
2y=-6x-8........y=-6x-8
2
-x+7 =-6x-8 ......2(-x+7)=2(-6x-8).....-2x+14=-12x-16...-2x+12x=-16-14
2 2
10x=-30.......x=-30/10.......x= -3
si x= -3........2y=7-x.......2y=7-(-3)......2y=7+3.....2y=10.....y=10/2....y=5
respuesta x= -3 y=5
.................................................................
2x+3y=1
x+y=-2
1(2x+3y=1)...........2x+3y=1
-2(x+y=-2)............-2x-2y=4
y=5
si y=5.....x+y=-2......x+5=-2......x=-2-5........x=-7
respuesta x= -7 y=5
....................................................
4y=3+x....................-x+4y=3
3x+7y=10.................3x+7y=10
3(-x+4y=3).........-3x+12y=9
1(3x+7y=10)........3x+7y=10
19y=19.....y=19/19......y=1
si y=1......4y=3+x.......4(1)=3+x.....4=3+x......4-3=x.......1=x
respuesta x=1 y=1
Respuesta dada por:
14
Buenas tades,
1)
a)
![\left \{ {{-7x-4y=-7 (1)} \atop {2x-y=2(2)}} \right. \\. \\ Ec (1): \\ 7x=7-4y \\ x=1- \frac{4}{7} y\\. \\ Ec (2): \\ 2x=2+y \\ x=1+ \frac{1}{2} y \\ . \\ x=x \\ 1- \frac{4}{7} y=1+ \frac{1}{2} y \\ y=0 \\ .\\ y\,\, en \,\,Ec(2): \\ 2x=2 \\ x=1 \left \{ {{-7x-4y=-7 (1)} \atop {2x-y=2(2)}} \right. \\. \\ Ec (1): \\ 7x=7-4y \\ x=1- \frac{4}{7} y\\. \\ Ec (2): \\ 2x=2+y \\ x=1+ \frac{1}{2} y \\ . \\ x=x \\ 1- \frac{4}{7} y=1+ \frac{1}{2} y \\ y=0 \\ .\\ y\,\, en \,\,Ec(2): \\ 2x=2 \\ x=1](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7B-7x-4y%3D-7+%281%29%7D+%5Catop+%7B2x-y%3D2%282%29%7D%7D+%5Cright.++%5C%5C.+%5C%5C++Ec+%281%29%3A+%5C%5C+7x%3D7-4y+%5C%5C+x%3D1-+%5Cfrac%7B4%7D%7B7%7D+y%5C%5C.+%5C%5C++Ec+%282%29%3A+%5C%5C+2x%3D2%2By+%5C%5C+x%3D1%2B+%5Cfrac%7B1%7D%7B2%7D+y++%5C%5C+.+%5C%5C+x%3Dx+%5C%5C+1-+%5Cfrac%7B4%7D%7B7%7D+y%3D1%2B+%5Cfrac%7B1%7D%7B2%7D+y++%5C%5C+y%3D0++%5C%5C+.%5C%5C+y%5C%2C%5C%2C+en+%5C%2C%5C%2CEc%282%29%3A+%5C%5C+2x%3D2+%5C%5C+x%3D1)
Solución: x=1 ; y=0
b)
![\left \{ {{2y=7-x (1)} \atop {2y=-6x-8(2)}} \right. \\. \\ Ec(1)=Ec(2) \\ 7-x=-6x-8\\ 7x=15 \\ 5x= -15\\x=-3 \\ .\\ x\,\, en \,\,Ec(1): \\ 2y=7-(-3)\\ 2y=10\\y=5 \left \{ {{2y=7-x (1)} \atop {2y=-6x-8(2)}} \right. \\. \\ Ec(1)=Ec(2) \\ 7-x=-6x-8\\ 7x=15 \\ 5x= -15\\x=-3 \\ .\\ x\,\, en \,\,Ec(1): \\ 2y=7-(-3)\\ 2y=10\\y=5](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7B2y%3D7-x+%281%29%7D+%5Catop+%7B2y%3D-6x-8%282%29%7D%7D+%5Cright.+%5C%5C.+%5C%5C++Ec%281%29%3DEc%282%29+%5C%5C+7-x%3D-6x-8%5C%5C+7x%3D15+%5C%5C+5x%3D+-15%5C%5Cx%3D-3+%5C%5C+.%5C%5C+x%5C%2C%5C%2C+en+%5C%2C%5C%2CEc%281%29%3A+%5C%5C+2y%3D7-%28-3%29%5C%5C+2y%3D10%5C%5Cy%3D5+)
Solución: x=-3 ; y=5
2)
a)
![\left \{ {{2x+3y=1 (1)} \atop {x+y=-2(2)}} \right. \\. \\Ec(1)-2Ec(2): \\ y=5 \\ . \\ y\,\, en \,\,Ec(2): \\ x+5=-2 \\ x=-7 \left \{ {{2x+3y=1 (1)} \atop {x+y=-2(2)}} \right. \\. \\Ec(1)-2Ec(2): \\ y=5 \\ . \\ y\,\, en \,\,Ec(2): \\ x+5=-2 \\ x=-7](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7B2x%2B3y%3D1+%281%29%7D+%5Catop+%7Bx%2By%3D-2%282%29%7D%7D+%5Cright.+%5C%5C.+%5C%5CEc%281%29-2Ec%282%29%3A+%5C%5C+y%3D5+%5C%5C+.+%5C%5C+y%5C%2C%5C%2C+en+%5C%2C%5C%2CEc%282%29%3A+%5C%5C+x%2B5%3D-2+%5C%5C+x%3D-7)
Solución: x=-7 ; y=5
b)
![\left \{ {{-x+4y=3 (1)} \atop {3x+7y=10(2)}} \right. \\. \\3Ec(1)+Ec(2): \\ 19y=19 \\ y=1\\. \\ y\,\, en \,\,Ec(1): \\4(1)=3+x \\ x=1 \left \{ {{-x+4y=3 (1)} \atop {3x+7y=10(2)}} \right. \\. \\3Ec(1)+Ec(2): \\ 19y=19 \\ y=1\\. \\ y\,\, en \,\,Ec(1): \\4(1)=3+x \\ x=1](https://tex.z-dn.net/?f=%5Cleft+%5C%7B+%7B%7B-x%2B4y%3D3+%281%29%7D+%5Catop+%7B3x%2B7y%3D10%282%29%7D%7D+%5Cright.+%5C%5C.+%5C%5C3Ec%281%29%2BEc%282%29%3A+%5C%5C+19y%3D19+%5C%5C++y%3D1%5C%5C.+%5C%5C++y%5C%2C%5C%2C+en+%5C%2C%5C%2CEc%281%29%3A+%5C%5C4%281%29%3D3%2Bx+%5C%5C+x%3D1)
Solución: x=1 ; y=1
1)
a)
Solución: x=1 ; y=0
b)
Solución: x=-3 ; y=5
2)
a)
Solución: x=-7 ; y=5
b)
Solución: x=1 ; y=1
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