Answer:
x = 3.83
y = 0.84
Step-by-step explanation:
Given;
[tex]\frac{2}{x-3y} = 1\frac{1}{2} (\frac{5}{x+y} ) ---(i)\\\\3x -5y = 7---(ii)\\[/tex]
Solving the simultaneous equation by elimination method;
[tex]\frac{2}{x-3y} = \frac{3}{2} (\frac{5}{x+y} )\\\\\frac{2}{x-3y} =\frac{15}{2x+2y} \\\\15(x-3y) = 2(2x +2y)\\\\15x - 45y = 4x + 4y\\\\11x - 49y = 0 --(i)\\\\3x - 5y = 7 --(ii)\\\\3: \ \ 33x -147= 0 ---(iii)\\\\11: -(33x -55y =77) ---(iv)\\{-----------} \\ (iii\ + \ iv): -92y = -77\\\\y = \frac{77}{92} = 0.84 \\\\solve \ for \ x \ using \ (ii)\\\\3x - 5(\frac{77}{92} ) = 7\\\\3x - \frac{385}{92} = 7\\\\3x = 7 + \frac{385}{92}\\\\3x = \frac{644 + 385}{92} \\\\3x = \frac{1029}{92} \\\\[/tex]
[tex]3x = \frac{1029}{92} \\\\x = \frac{1029}{92 \times 3}\\\\x = 3.73[/tex]
(ii) By substitution method;
[tex]11x - 49y = 0 --(i)\\\\3x - 5y = 7 --(ii)\\\\from \ (i), 11x = 49y\\\\x = \frac{49y}{11} \\\\substitute \ x \ in (ii);\\\\3(\frac{49y}{11} ) - 5y = 7 \\\\\frac{147y}{11} - 5y = 7\\\\\frac{147y - 55y}{11}= 7\\\\92y = 77\\\\y = \frac{77}{92} = 0.84 \\\\solve \ for \ x;\\\\x = \frac{49}{11} (\frac{77}{92} ) = 3.73[/tex]
