Question

A system of equations is graphed on the coordinate plane.

y = −4x − 6
y = −4x + 7
How would you classify this system of equations?
1 - Consistent
2 - Consistent and Coincident
3 - Inconsistent

Answer 1

The system of equations y = -4x - 6 and y = -4x + 7 are parallel and do not intersect, making the system inconsistent.

The correct answer is option 3- Inconsistent.

Step-by-step explanation:

The given system of equations is:

• y = -4x - 6
• y = -4x + 7

Both equations have the same slope of -4, which is the coefficient of x. However, they have different y-intercepts: -6 and +7, respectively. Since they have the same slope but different y-intercepts, the lines are parallel to each other and will never intersect. Therefore, there is no solution to this system of equations, and it is classified as inconsistent.