Line AB, with equation: 3x + 2y - 1 = 0, intersects line CD, with equation 4x - 6y -10 = 0. Find the point, P, where the two lines intersect.
Let eqn. 1 be: 3x + 2y - 1 = 0 & Let eqn. 2 be: 4x - 6y -10 = 0
Multiply eqn. 1 by a factor of 3, and add the two eqautions together. (This eliminates y from the equation)
This gives: 9x + 6y - 3 = 0
+ 4x - 6y - 10 =0
This gives the equation: 13x - 13 = 0, so 13x = 13, and therefore x =1.
Substitute this value of x into either eqn. 1 or eqn. 2. (I will use eqn. 1 for this example) 3(1) + 2y - 1 = 0. This can be rearranged to give 2y = -2, and hence y = -1.
Therefore, point P is at (1, -1).
KS
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