Please solve by graphing. Indicate whether each system is independent,
inconsistent, or dependent. Thank you for your help
1. y = 3x - 4
y = -2x + 1
2. 2x - 3y = 12
3y - 2x = -12
They are independent if their graphs (which are straight lines) intersect in a
point, and the two coordinates of that point of intersection will represent the
solution to that system.
They are inconsistent if their graphs (straight lines) are parallel, which
means they don't intersect and therefore there can have no solution.
They are dependent if they coincide
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1.
y = 3x - 4
y = -2x + 1
Get a few points on each
For y = 3x - 4 plot (-1, 7), (0, -4), (2, 2)
For y = -2x + 1 plot (-1, 3), (0, 1), (2, -3)
Draw the two lines:
The look like they cross at the point (x, y) = (1, -1)
So they are independent
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2.
2x - 3y = 12
3y - 2x = -12
Get a few points on each
For 2x - 3y = 12 plot (0, -4), (3, -2), (6, 0)
For 3y - 2x = -12 plot (-3, -6), (-6, -8), (9, 2)
Draw the two lines:
You only see one line. That's because they coincide,
So the system of equations is dependent. There are infinitely many solutions
because every point on them represents a solution.
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3.
You didn't have a system that turned out to be inconsistent. Here's one:
2x - y = 4
2y - 4x = 6
Get a few points on each
For 2x - y = 4 plot (0, -4), (2, 0), (4, 4)
For 2y - 4x = 6 plot (-1, 1), (-3, -3), (0, 3)
Draw the two lines:
They are parallel, so they are inconsistent and have no
solution.
Edwin
AnlytcPhil@aol.com
