Algebra
posted by Anonymous
How many solutions does this system of equations have?
y = 4x + 3 and 2y  8x = 3
One, two, infinitely many, or no solutions? My answer is no solutions.

Damon
y = 4 x + 3
y = 4 x + 3/2
two lines with the same slope but different y axis intercepts. They never cross each other and therefore there is no solution to this problem. 
Anonymous
Thanks. I have a couple more:
x = 4y + 4 and 2x + 8y = 8
Answer: Infinitely many solutions
x  3y = 15 and 3x  9y = 4
Answer: Infinitely many solutions
y  5x = 6 and 3y  15x = 12
Answer: One solution 
Damon
x  3y = 15 and 3x  9y = 4
x  3 y = 4/3
Same slope, never cross NO solutions !
Answer: Infinitely many solutions DIASAGREE
y  5x = 6 and 3y  15x = 12
y  5 x = 4
AGAIN, they are NOT the same. They are PARALLEL and never cross NO solutions
same m = slope = either the same (infinite solutions of parallel (different y intercept) which means ZERO solutions
Answer: One solution NO! 
Anonymous
Seems like both have no solutions. I went a bit off in my calculation. I see now.

Damon
When in doubt, sketch a graph
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