Question 277922: I am not sure how to work these three problems :
For the systems of linear equations in questions 1-3
Determine how many solutions exist
Use either elimination or substitution to find the solutions (if any)
Graph the two lines, labeling the x-intercepts, y-intercepts, and points of intersection
1.y = 2x + 3 and y = -x - 4
2.2x + 3y = 8 and 3x + 2y = 7
3.2x + 3y = 8 and 3x + 2y = 7
Answer by nabla(475)   (Show Source):
You can put this solution on YOUR website! Think of the graphs of lines in the plane.
You have three cases:
1) The lines cross once.
2) The lines never cross.
3) The lines always cross (i.e. they are the same).
From this argument you will see the number of solutions will be per case:
1) Exactly one point (a,b).
2) No points.
3) Infinitely many points.
So, what you want to do is determine whether (per each case):
1) The lines meet neither (2) nor (3) below.
2) The lines have same slope but different y-intercept.
3) The lines have the same slope and same y-intercept.
Now, recall this form of a line: y=mx+b . m is the slope and b is the y intercept (where x=0). So given these facts you can determine the number of solutions.
If a unique solution exists, you can find it via substitution (solve one equation for x or y and put that into the spot for x or y in the other equation) or elimination (subtracting a multiple of one equation from the other to eliminate a variable).
Finally, you can graph each line using the form of a line I present above. Moreover, you can plot a few values by picking an x and finding what y will be for that value, as lines are defined for all real numbers!
Hope this helps. If you want a particular solution for one of these problems, please contact me at enabla@gmail.com
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