One equation in a system of linear equations is y=2x+1 a. write a second equation so that (1,3) is the only solution of the system

b. Write a second equation so that the system has infinitely many solutions

c. Write a second equation so that the system has no solutions

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Step-by-step explanation:

Given equation:

a. write a second equation so that (1,3) is the only solution of the system

To have only one solution the equation must have a different slope.

Let it be 10, then the y-intercept of y = 10x + b is:

And the equation:

b. Write a second equation so that the system has infinitely many solutions

To have infinitely many solutions, both equations must be same:

c. Write a second equation so that the system has no solutions.

To have no solutions, the equations must have same slope but different y-intercepts:

michael scott & dwight schrute

step-by-step explanation:

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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)