can someone please show me how to solve this problem simultaneous.

there are two patterns created in the string design:

-the intersection of consecutive lines

-an envelope formed by the lines themselves, the equation for the envelope is difficult to obtain. the coordinates of the points of the intersection between consecutive lines is much easier to obtain. the intersection between the first two lines can be determined using simultaneous equations.

the equation to the first line is:

the equation to the second line is:

can you solve these equations simultaneously to determine the first point of the intersection?

solve the second pair of the equations simutalneously?