Question

line 1: y=-x - 3
line 2: y=-x + 3
this system of equations is:
consistent independent
consistent dependent
inconsistent
this means the system has:
a unique solution
solution: ( , )
no solution
infinitely many solutions

Explanation:

Step1: Identify the slopes and y - intercepts

The first line is $y=-x - 3$, with slope $m_1=-1$ and y - intercept $b_1=-3$. The second line is $y=-x + 3$, with slope $m_2=-1$ and y - intercept $b_2 = 3$.

Step2: Determine the type of system

Since $m_1=m_2=-1$ and $b_1
eq b_2$, the lines are parallel. Parallel lines do not intersect. A system of equations representing parallel lines is inconsistent.

Step3: Find the number of solutions

An inconsistent system of equations has no solution.

Answer:

This system of equations is: inconsistent
This means the system has: no solution