Question 1073739: 3x+4y=-4
x-2y=2
Determine whether the system has no solution, infinite or one solution.
CAN SOMEONE PLEASE SHOW ME HOW TO DO THIS?? THANKS!!
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! There are number of ways, but one way is to observe that the two equations represent lines in the x-y plane.
Writing in standard form we have:
y = (-3/4)x - 1 [1]
y = (-1/2)x - 1 [2]
We can see right away that the y-intercept of both of these lines is -1.
Thus the two lines intersect at the point (0,-1).
Since the lines have a different slope, they intersect at only this one point.
Therefore there is one solution.
If the lines also had the same slope, then there would be infinitely many solutions.
Obviously, if there were no intersection points, the lines would be parallel, and thus the system would have no solution.
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