Question

Examine the system of equations. Do you think the lines will intersect? Explain. y = 2x – 7 y = x – 7

Answer 1

Sample Response/Explanation: Yes, the lines will intersect because the slopes are different. Also, both lines have a y-intercept of -7, so they both include the point (0, –7).

Which did you include in your response? Check all that apply.

The lines will intersect.

The slopes are different.

The point (0, –7) lies on both lines.

Answer 2

Answer:

Indeed. The system of equations has a solution at point (0, -7).

Step-by-step explanation:

A system of linear equations is consistent only if exist a solution. Let equalize each expression to eliminate y and determine if a solution for x exist. That is:

$2\cdot x - 7 = x - 7$

$2\cdot x - x = 7 - 7$

$x = 0$

Therefore, the system of linear equations has a solution at point (0, -7).