Determine whether the System of equations 3x+y=-5; 3y+15=-9x

So, let's do it by isolating

y

in the first equation.

3

x

−

2

y

=

10

−

2

y

=

10

−

3

x

y

=

−

5

+

3

x

2

Now you just have to substitute this value of

y

in the second equation.

5

x

+

3

(

−

5

+

3

x

2

)

=

15

5

x

−

15

+

9

x

2

=

15

1

x

2

=

30

x

=

30

⋅

2

=

60

x

=

60

If

x

=

60

and the value of

y

is given by

y

=

−

5

+

3

x

2

, then:

y

=

−

5

+

3

(

60

)

2

=

−

5

+

180

2

=

−

5

+

90

=

85

5050

hope this !

hello from mrbilldoesmath!

answer:   (7x + 6y) ( 49x^2 - 42xy + 36y^2)

discussion:

in general, the factorization of a^3 + b^3 is

a^3 + b^ 3 = (a + b) ( a^2 - ab + b^2)

in our case note that 343 = 7^3 and 216 = 6^3 so the equation becomes:

343x^3 + 216y^3 = (7x)^3 + (6y)^3

if you think of a (above) as 7x and b as 6y the factorization becomes

343x^3 + 216y^3 =

((7x + 6y) (   (7x)^2 - 7x*6y + (6y)^2)   =

(7x + 6y) ( 49x^2 - 42xy + 36y^2)

you,

mrb

(a + b) (a^2 - a b + b^2)