In the figure AB = BD, A and D are equidistant from C. If AB \$= x\$, BD \$= 2y - 1\$, AC \$= 4x - 8\$ and DC \$= x- 5y\$, find the values of x and y.

A) \$x = 5\$ and \$y = 4\$

B) \$x = 1\$ and \$y = 1\$

C) \$x = 3\$ and \$y = 2\$

D) \$x = 5\$ and \$y = 3\$

ABC is a right angle triangle, right angled at B. BD is perpendicular to AC and D is the mid-point of AC. If AB \$= 4x\$, BC \$= 7 - 3y\$, AD \$= 5y\$ and DC \$= 8 - 3x\$, find the values of x and y.

A) \$x = 5\$ and \$y = 4\$

B) \$x = 3\$ and \$y = 2\$

C) \$x = 1\$ and \$y = 1\$

D) \$x = 5\$ and \$y = 3\$

F is the mid-point of DE, AF is perpendicular to DE, and D and E are equidistant fron A. If AD \$= x\$, DF \$= 3x\$, FE \$= 9 -y\$ and AE \$= y - 1\$, find the values of x and y.

A) \$x = 5\$ and \$y = 4\$

B) \$x = 3\$ and \$y = 2\$

C) \$x = 1\$ and \$y = 6\$

D) \$x = 2\$ and \$y = 3\$

ED is perpendicular to AC, B is the mid-point of ED and AC, and AD = EC. If EB \$= 2y - 5\$, DB \$= 5 - 2x\$, EC \$= 3x + y\$ and DA \$= 9\$, find the values of x and y.

A) \$x = 2\$ and \$y = 3\$

B) \$x = 3\$ and \$y = 2\$

C) \$x = 8\$ and \$y = 5\$

D) \$x = 3\$ and \$y = 4\$

In the figure B is the mid-point of AC and DE, and AD = EC. If AD \$= x - 3\$, CE \$= 6 - 3y\$, DB \$= 2x + 2y\$ and EB \$= 10\$ find the values of x and y.

A) \$x = 5\$ and \$y = 4\$

B) \$x = 3\$ and \$y = 2\$

C) \$x = 3\$ and \$y = 3\$

D) \$x = 5\$ and \$y = 3\$