Question

Which of the following graphs best represents the solution to the pair of equations below? (4 points)

y = x + 1
y = −x − 1

Group of answer choices

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 and 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.

A coordinate plane is shown with two lines graphed. One line passes through the y axis at negative 1 and the x axis at 1. The other line passes through the y axis at 1 and the x axis at 1. The lines intersect at 1 comma 0.

Answer 1

Option B is the correct option.

Explanation:

We are given the system of equations by,

y=x+1y=x+1 and y=-x-1y=−x−1 .

Adding both the equation, we get,

2y=02y=0 i.e. y= 0

Substituting y= 0 in any equation gives,

0=x+10=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+1y=x+1 implies y=0+1y=0+1 i.e. y= 1

y=-x-1y=−x−1 implies y=-0-1y=−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.