Mark M. answered • 05/20/15
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Mathematics Teacher - NCLB Highly Qualified
-5x + 4y = 2
10x - 8y = 4 Multiply both sides of top equation by 2
-10x + 8y = 4
10x - 8y = 4 Add the two equations
0 = 4 No common solution
∅
Andrew M.
Note the slopes of the 2 lines in question:
L1 -5x+4y=2 L2 10x-8y=4
solve for y solve for y
4y = 5x +2 -8y = -10x + 4
y = 5/4 x + 1/2 y = 10/8 x -4/8
y = 5/4 x - 1/2
These have the same slope m = 5/4 but different y intercepts..
L1 has y intercept at (0,1/2) and L2 has y intercept (0,-1/2)
Since the lines are parallel then if one point was common then all points would
be common and they would be the same line. Since this is not true then they
have no common points so the intersection is the empty set
I = ∅
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05/21/15
Andrew M.
05/21/15