Which equation has the solutions x= -3 +- sqrt 3i /2

For you to graph each system, you need to always get y by itself. If there is 2y , then divide both sides by 2 , etc.

For x+y=6 , you would subtract x so that it equals:
y=−x+6

For the other one: x−y=4 add y to both sides and then subtract 4 to get: x−4=y. which is also: y=x−4

To determine the possible solutions, I am uncertain if you mean where they intersect or possible solutions for x and y for each equation individually.

If you need to calculate the point of intersection, set them equal to each other:

y=y , therefore: x−4=−x+6 ,

2x=10
x=5
y=1

Or you can draw the graphs by plotting points and find where the lines intersect

An inconsistent system of equations is a system of equations with no solution. We can determine if our system is inconsistent in three ways: graphing, algebra, and logic. Graphs of an inconsistent system will have no points of intersection.

I hope you get the answer.

Let me know if you need more details