(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) 
\(/BC/^{2} = 36^{2} + 48^{2}\)
\(/BC/^{2} = 1296 + 2304 = 3600\)
\(/BC/ = \sqrt{3600} = 60 cm\)
\(/AC/^{2} = /BC/^{2} + /AB/^{2}\)
\((y + 48)^{2} = 60^{2} + 36^{2} + y^{2}\)
\(y^{2} + 96y + 2304 = 3600 + 1296 + y^{2}\)
\(96y = 3600 + 1296 - 2304 = 2592\)
\(96y = 2592 \implies y = \frac{2592}{96} = 27 cm\)