What is true about the solution for the following system of linear equations?

Question

y=x+3


y=x+7


(4 points)
Responses

The two lines would not intersect because they have the same slopes but different y-intercepts. Therefore there is no solution.
The two lines would not intersect because they have the same slopes but different y-intercepts. Therefore there is no solution.

The two lines intersect at point (3,7). Therefore the solution is (3,7).
The two lines intersect at point (3,7). Therefore the solution is (3,7).

The two lines lie exactly on top of one another. Therefore there are infinitely many solutions.

Answer 1

To analyze the system of linear equations:

1. \( y = x + 3 \)
2. \( y = x + 7 \)

We start by observing the slopes and y-intercepts of these equations.

• Both lines have a slope of 1 (the coefficient of \( x \) is the same in both equations).
• The first line has a y-intercept of 3, while the second line has a y-intercept of 7.

Since the slopes are the same but the y-intercepts are different, it means that these two lines are parallel and will never intersect.

Thus, the statement "The two lines would not intersect because they have the same slopes but different y-intercepts. Therefore there is no solution." is true.

Therefore, the answer is:

The two lines would not intersect because they have the same slopes but different y-intercepts. Therefore there is no solution.