For the three-part question that follows, provide your answer to each part in the given workspace. Identify each part with a coordinating response.

Question

Part A: Discuss how to determine if a point, (x,y), is a point of intersection for 2 lines given the equations of the lines.

Part B: Determine whether the lines given by the following equations intersect at (-1/4,3/4). Show all work. 4x+8y=5 x-3y=-3

Part C: Determine whether the lines given by the following equations intersect at (1/2,-1/8). Show all work. 3x-4y=2 y=1/4x-1/4

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Answer 1

To check is a point is an intersection of two lines, put x and y into both equations and see if they check out.

4(-1/4) + 8(3/4) = 5 -> -1 + 6 = 5 (Yes.) (-1/4) - 3(3/4) = -3 -> -1/4 - 9/4 = -10/4 (No.) Part B is not correct.

3(1/2)-4(-1/8)=2 -> 3/2 + 1/2 = 2 (Yes.) (-1/8) = (1/4)(1/2)-(1/4) -> -1/8 = 1/8 - 1/4 (Yes.) Part C is correct.