SOLUTION: Please help me with these problems, I'm really confused. :( Thank you! How many solutions do the following systems of equations have? Justify your answer. a. -2x + 4y = 1, 3x

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Question 936600: Please help me with these problems, I'm really confused. :( Thank you!
How many solutions do the following systems of equations have? Justify your answer.
a. -2x + 4y = 1, 3x - 6y = 9
b. x + y = 8, 2x + 2y = -1
c. y = (1/2)x - 4, x - 2y = 8

Answer by josgarithmetic(39617) (Show Source):
You can put this solution on YOUR website!
Are slopes of a pair of equations equal or unequal?
Slopes equal, means the pair of lines either parallel or identical; if parallel but equations are not identical, then no point of intersection. If equations of the lines are identical, then this just means that the pair is not really a pair, so just are the same line.

If the slopes are unequal, then the pair intersect in exactly one point.

Convert each pair of equations into the same form and simplify. Suggested form could be slope-intercept. You could choose standard form if you prefer, as long as you know what the parts of the equational form mean.

(b):
and
Simplified into
and ;
Same slope, but different constant value for their right-hand members. These lines are parallel and have no solution as a system. They do not intersect.