Expert: Sherman D. - 7/9/2005

Question
Which system has infinitely many solutions? y=2x+6, y
-8x=21....4x-4y=4, x-y=1....4x+2y=5, x-2y=9...or none of
these.

Answer
ANS :
4x - 4y = 4
x - y = 1

If the 2 equations end up with the same slope and the same y-intercept, then the problems have infinate solutions.

y = 2x + 6
y - 8x = 21

y - 8x = 21
y = 8x + 21

so this gives you

y = 2x + 6
y = 8x + 21

Different slope, therefore these problems have one solution.

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4x - 4y = 4
x - y = 1

4x - 4y = 4
-4y = -4x + 4
y = x - 1

x - y = 1
-y = -x + 1
y = x - 1

so this gives you

y = x - 1
y = x - 1

These problems have the same slope and the same y-intercept, therefore these problems have Infinate Solution.

---------------------

4x + 2y = 5
2x - 2y = 9

4x + 2y = 5
2y = -4x + 5
y = -2x + (5/2)

2x - 2y = 9
-2y = -2x + 9
y = x - (9/2)

this gives you

y = -2x + (5/2)
y = x - (9/2)

different slopes and different y-intercepts, therefore this problem has One Solution.