(a) Solve the simultaneous equation : (6y + 5x = 12 ; 4y – 3x = 11).
(b)
In the diagram, ADC is a straight line. /CD/ = 48 cm, /BD/ = 36 cm and /AD/ = y cm. Find the value of y.
Explanation
(a) (6y + 5x = -12 … (1))
(4y – 3x = 11 … (2))
Multiply (1) by 2 and (2) by 3,
(12y + 10x = -24 … (1a))
(12y – 9x = 33 … (2a))
((1a) – (2a) : 19x = -57 implies x = -3)
(4y – 3(-3) = 11 implies 4y + 9 = 11)
(4y = 2 implies y = frac{1}{2})
(b)
(/BC/^{2} = 36^{2} + 48^{2})
(/BC/^{2} = 1296 + 2304 = 3600)
(/BC/ = sqrt{3600} = 60 cm)
(/AC/^{2} = /BC/^{2} + /AB/^{2})
((y + 48)^{2} = 60^{2} + 36^{2} + y^{2})
(y^{2} + 96y + 2304 = 3600 + 1296 + y^{2})
(96y = 3600 + 1296 – 2304 = 2592)
(96y = 2592 implies y = frac{2592}{96} = 27 cm)