Hey there!
1.) The correct answer would be none since when lines are parallel to each other in a system of equations, there is no point of intersection, meaning there are no solutions.
2.) The correct answer would be one solution because there is one point of intersection which would be the answer to the system.
3.) The correct answer would be infinitely many because this means that both equations graph to be the same line. This means that any value can be the answer and result with a valid answer.
4.) To start, first you must graph the two equations and find the point of intersection. When you graph each line, notice that both the lines intersect on one point: (1,-2)
The red line is y=x-3
The blue line is y=-2x
Therefore, (1,-2) would be your answer.
5.) For this one, first convert both equations to slope intercept form, or y=mx+b.
To turn x+y=-2 in this form, subtract x from both sides to get y=-x-2
To turn y-2x=1 into this form, add -2x to both sides to get y=2x+1
Orange line is x+y=-2
Purple line is y-2x=1
Now, graph the two lines and you get (-1,-1) as your answer.
