Question

Line A is represented by the equation given below:

x + y = 4

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

4x + 4y = 4
4x + y = 4
2x + 2y = 8
x + y = 8

Answer 1

To have infinitely many solutions they must describe the same line. So any multiple or fraction of the reference line would indeed describe the same line, and thus "intersect" at each and every of an infinite number of points.

2(x+y=4)

2x+2y=8 (is the same line as x+y=4)

Answer 2

C.
`2x+2y=8`

Explanation:

We have been given equation of line A as
`x+y=4`. We are asked to choose the equation line B from our given choices, so that set of equations has infinitely many solutions.

We know that a set of equations has infinitely many solutions, when they represent same line or they are coincident.

Upon looking at our given choices, we can see that option C is the correct choice as we will get same line, when we will divide equation by 2 as:

`2x+2y=8`

`(2x)/(2)+(2y)/(2)=(8)/(2)`

`x+y=4`

Therefore, option C is the correct choice.