Question

Which of the following graphs best represents the solution to the pair of equations below? y = x + 1 y = −x − 1 A coordinate plane is shown with two lines graphed. One line passes through the y axis at 1 and the x axis at 1. The other line passes through the y axis at 1 and the x axis at negative 1. The lines intersect at 0 comma 1. A coordinate plane is shown with two lines graphed. One line passes through the y axis at 1 and the x axis at negative 1. The other line passes through the y axis at negative 1 and the x axis at negative 1. The lies intersect at negative 1 comma 0. A coordinate plane is shown with two lines graphed. One line passes through the y axis at negative 1 and the x axis at negative 1. The other line passes through the y axis at negative 1 and the x axis at 1. The lines intersect at 0 comma negative 1.

Answer 1

The best and most correct answer among the choices provided by the question is the fourth choice. The graph of the two equations is "A coordinate plane is shown with two lines graphed. One line passes through the y axis at negative 1 and the x axis at negative 1. The other line passes through the y axis at negative 1 and the x axis at 1. The lines intersect at 0 comma negative 1." I hope my answer has come to your help. God bless and have a nice day ahead!

Answer 2

Option B is the correct option.

Explanation:

We are given the system of equations by,

`y=x+1` and
`y=-x-1`.

Adding both the equation, we get,

`2y=0` i.e. y= 0

Substituting y= 0 in any equation gives,

`0=x+1` i.e. x= -1

Thus, the solution of the equations is the point (-1,0).

That is, the graph of both the equations must intersect at the point (-1,0).

Further, substituting x= 0 in the equations, we get,

`y=x+1` implies
`y=0+1` i.e. y= 1

`y=-x-1` implies
`y=-0-1` i.e. y= -1.

So, one line passes through y-axis at (0,1) and other line passes through y-axis at (0,-1).

Hence, option B is the correct answer.