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| 1. |
Solve 2 (ax-by) + a + 4b=02 (ax-ay) + b- 4a = 0 |
| Answer» The given equations may be written as2(ax - by) + (a + 4b) = 02ax - 2by + (a + 4b) = 02ax - 2by = - a - 4 b ... (i)and 2(bx + ay) + (b - 4a) = 0(2bx + 2ay) + (b - 4a) = 02bx + 2ay = 4a - b. ... (ii)Multiplying (i) by a and (ii) by b and adding, we get(2a2+ 2b2) x = (-a2\xa0- b2){tex} \\Rightarrow 2 \\left( a ^ { 2 } + b ^ { 2 } \\right) x = - \\left( a ^ { 2 } + b ^ { 2 } \\right) {/tex}{tex}\\Rightarrow x = \\frac { - 1 } { 2 }{/tex}Putting x = -{tex}\\frac 12{/tex}\xa0in (i), we get{tex}2 a \\times \\left( \\frac { - 1 } { 2 } \\right) - 2 b y = - a - 4 b{/tex}{tex}\\Rightarrow \\quad - a - 2 b y = - a - 4 b{/tex}{tex}\\Rightarrow \\quad 2 b y = 4 b {/tex}{tex}\\Rightarrow y = \\frac { 4 b } { 2 b } = 2{/tex}Hence, x =\xa0{tex}\\frac{-1}{2}{/tex} and y = 2 | |