Answer:
2.) Infinitely many solutions
3.) No solutions
Step-by-step explanation:
To solve systems of equations graphically, you need to find where they intersect
2.) First put each equation in the form y=mx+b
x-y=6 -> y= x-6
2x=12+2y -> y= x-6
Then, graph each line
Since we have the same equation, the lines are on top of each other so there are infinitely many solutions as they intersect everywhere.
To check, plug a point in from the graph into both equations and you should get 0=0
3.) First put each equation in the form y=mx+b
1/2x-y=4 -> y=1/2x-4
2y=x+6 -> y=1/2x+3
Then, graph each line
Since the lines have the same slope but a different y intercept, the lines are parallel. Therefore, there are no solutions as they do not intersect.
To check your answer, you would one equation as the y in the other equation.
2(1/2x-4)=x+6, then solve for x
Then plug that x into the original equations, and you'll see they are not equal. Hope that helps!