Question

Resuelve y comprueba las siguientes ecuaciones con el metodo de igualación.

A) 10x + 3y = - 27
X + y = - 9

B) x + 5y = 3
2x + 7y = 0

C) 3x + 2y =60
6x - 7y = - 45​

Answer 1

Respuesta:

A) x=10. y=-9

B) x=-7. y=2

C) x=10, y=15

Explicación paso a paso:

A)

$10x+3y=-27=10x=-27-3y\\x+y=-9=x=-9-y\\x=\frac{-27-3y}{10}=x=\frac{-9-y}{1}\\1(-27-3y)=10(-9-y)\\-27-3y=-90-10y\\10y-3y=-90+27\\7y=-63\\y=-\frac{63}{7}=y=-9\\\\10x+3(-9)=-27\\10x-27=-27\\10x=-27+27\\10x=x=10$

B)

$x+5y=3=x=3-5y\\2x+7y=0=2x=-7y\\x=\frac{3-5y}{1}=x=\frac{-7y}{2}\\2(3-5y)=1(-7y)\\6-10y=-7y\\7y-10y=-6\\-3y=-6\\y=\frac{6}{3}=y=2\\\\x+5(2)=3\\x+10=3\\x=3-10\\x=-7$

C)

$3x+2y=60=3x=60-2y\\6x-7y=-45=6x=-45+7y\\x=\frac{60-2y}{3}=x=\frac{-45+7y}{6}\\6(60-2y)=3(-45+7y)\\360-12y=-135+21y\\-21y-12y=-135-360\\-33y=-495\\y=\frac{495}{33}=y=15\\\\3x+2(15)=60\\3x+30=60\\3x=60-30\\3x=30\\x=\frac{30}{3}=x=10$

Espero te ayude mucho, corona por favor

Answer 2

Respuesta:

A) y= -9   x= 0

B) y= 2   x= -7

C) y= 15   x= 10

Explicación paso a paso:

A) 10x + 3y = - 27

X + y = - 9

x = (- 27  - 3y) / 10

x = - 9 - y

x = x

(- 27  - 3y) / 10 = -9 - y

10*((- 27  - 3y) / 10 = -9 - y)

-27  - 3y= -90 - 10y

- 3y + 10y= -90 +27

7y= - 63

y= -63 / 7

y= -9

10x + 3y = - 27

10x + 3(-9) = - 27

10x - 27 = - 27

10x= -27 + 27

10x= 0

x= 0

Comprobación:

x + y = - 9

0 + (-9) = -9

0 - 9 = -9

-9 = -9

B) x + 5y = 3

2x + 7y = 0

x = 3  - 5y

x = (0 - 7y) / 2

x=x

3 - 5y = (0 - 7y) / 2

2*(3 - 5y = (0 - 7y) / 2)

6 - 10y = 0 - 7y

-10y + 7y = -6

-3y = -6

y= (-6) / (-3)

y= 2

x + 5y = 3

x + 5(2) = 3

x + 10 = 3

x= 3 - 10

x= -7

Comprobación:

2x + 7y = 0

2(-7) + 7(2) = 0

-14 + 14 = 0

0 = 0

C) 3x + 2y =60

6x - 7y = - 45​

x= (60 -2y) / 3

x = (-45​ + 7y) / 6

x=x

(60 -2y) / 3 = (-45​ + 7y) / 6

2*((60 -2y) / 3) = (-45​ + 7y) / 6

6*((120 -4y) / 6) = (-45​ + 7y) / 6)

120 -4y = -45​ + 7y

-4y - 7y = -45 - 120

-11y= -165

y= (-165) / (-11)

y= 15

3x + 2y =60

3x + 2(15) =60

3x + 30 =60

3x= 60 - 30

3x= 30

x= 30 / 3

x= 10

Comprobación:

6x - 7y = - 45

6(10) - 7(15) = - 45

60 - 105 = - 45

-45 = -45