Which of the following pairs of linear equations are consistent/inconsistent? Ifconsistent, obtain the solution graphically

To determine if a pair of linear equations is consistent or inconsistent, follow these steps:

1. Break Down the Problem

   You need to analyze the given pairs of linear equations. For each pair, we need to check their graphs to see if they intersect (consistent) or are parallel (inconsistent).

2. Relevant Concepts

   • Consistent equations: These equations have at least one solution (their graphs intersect).
   • Inconsistent equations: These equations have no solution (their graphs are parallel).

3. Analysis and Detail

   For each pair of equations, perform the following steps:

   • Convert the equations into the slope-intercept form $y = mx + b$ to determine their slopes ($m$) and y-intercepts ($b$).
   • Compare the slopes:
     • If the slopes are equal but the y-intercepts are different, the equations are inconsistent.
     • If the slopes are equal and the y-intercepts are also equal, the equations are consistent and represent the same line.
     • If the slopes are different, the equations are consistent and intersect at one point.

4. Verify and Summarize

   After determining the consistency or inconsistency, you can graph the equations to visualize their relationship.

Final Answer

After carrying out the necessary calculations and plotting the equations on a graph, you will be able to conclude whether each pair is consistent or inconsistent and, if consistent, the point of intersection.