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Can someone verify that the answer is A? 

Line H is represented by the following equation: 2x + 2y = 8

What is most likely the equation for line K so the set of equations has infinitely many solutions?

A x + 2y = 2
B x + y = 4
C 2x + y = 6
D x − y = 8

Respuesta :

student100500
The answer is A because:...
2x + 2y = 8
You need to simplify it by getting either the x or the y by itself so you need to divide everything by two.
= x + y = 4
I hope this helped!!:)

Answer:

Option: B is the correct answer.

          B.    x+y=4

Step-by-step explanation:

The equation of the line H is given by:

                 [tex]2x+2y=8[/tex]

i.e. on dividing both the side of the equation by 2 we get:

                   [tex]x+y=4--------(1)[/tex]

Now, in order for a system to have infinite many solution the two lines must intersect infinite times.

A)

[tex]x+2y=2[/tex]

Now, when we subtract equation(1) from this equation we have:

[tex]y=-2[/tex]

and

[tex]x=6[/tex]

i.e. the solution is :  (6,-2)

i.e. the system has a unique solution.

B)

[tex]x+y=4[/tex]

This equation is similar to equation (1).

Hence, the system has infinite many solution.

C)

[tex]2x+y=6[/tex]

When, we subtract equation (1) from this equation  we have:

[tex]x=2[/tex]

and

[tex]y=2[/tex]

Hence, the system has a unique solution.

D)

[tex]x-y=8[/tex]

On adding this equation to equation (1) we get:

[tex]2x=12\\\\i.e.\\\\x=6[/tex]

and

[tex]y=-2[/tex]

Hence, the solution is unique i.e. (6,-2)

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