Question

A system of equations is graphed on the coordinate plane.

y=−2x−3

y=−2x+2

How would you classify this system of equations?
Question 5 options:


Consistent


Consistent and Coincident


Inconsistent

Answer 1

Answer: Last option.

Explanation:

The equation of the line in Slope-Intercept form is:

`y=mx+b`

Where "m" is the slope and "b" is the y-intercept.

Given the first equation:

`y=-2x-3`

You can identify that:

`m_1=-2\\b_1=-3`

And given the second equation:

`y=-2x+2`

You can identify that:

`m_2=-2\\b_2=2`

Then, since:

`m_1=m_2\\\\b_1\\eq b_2`

You can conclude that the lines are parallel.

By defintion, when the lines of a system of equations are parallel, the system has No solution and it is classified as "Inconsistent".