Lines AB and CD intersect at E, Measure AED=110, measure DEB=3x+2y, measure BEC = 9x+y, and measure CEA=70. Find the values of x and y. check your answer. [only algebraic solution will be accepted]

Answer: first take AED and DEB as one equation. because both angles lie on the line AB they must both add to 180 degrees.

therefore; 3x + 2y + 110 = 180

also for BEC and CEA both must add to 180; 9x + y + 70 = 180

we now can solve them by simultaneous equations. to do this we can make the x terms equal or the y terms equal. in this case lets go for the x terms.

multiply the first equation by 3 (to make the x terms equal);

9x + 6y + 330 = 540 (remember you multiply everything by 3 not just the x).

so now you have 9x + 6y + 330 = 540

and 9x + y + 70 = 180

now you take equation 1 away from equation 2. the two 9x's cancel out and 6y - y = 5, and 330 - 70 = 260 and 540 - 180 = 360. this gives us;

5y + 260 = 360

solve for y; y = 20 degrees

now we just substitute in y in one of the original equations e. g.

3x + 2 (20) + 110 = 180

tidy that up and you'll get x = 10 degrees