(a) Solve for x and y in the following equations :
(2x – y = frac{9}{2})
(x + 4y = 0)
(b)
In the diagram, TA is a tangent to the circle at A. If (stackrelfrown{BCA} = 40°) and (stackrelfrown{DAT} = 52°), find (stackrelfrown{BAD}).
Explanation
(a) (2x – y = frac{9}{2} …. (1))
(x + 4y = 0 ……. (2))
From (2), x = – 4y. Put into (1), we have
(2(- 4y) – y = frac{9}{2})
(-8y – y = frac{9}{2} implies – 9y = frac{9}{2})
(y = frac{frac{9}{2}}{-9} = -frac{1}{2})
(x = – 4y = -4(-frac{1}{2}))
(x = 2)
((x, y) = (2, -frac{1}{2}))
(b)
In (Delta ACD, stackrelfrown{ACD} = 52° ) (stackrelfrown{ACD} = stackrelfrown{DAT})
(therefore stackrelfrown{BCD} = 40° + 52° = 92°)
Note (stackrelfrown{BCD}) and (stackrelfrown{BAD}) are supplementary = 180°
(therefore stackrelfrown{BAD} = 180° – 92° = 88°)