दो चर वाले रैखिक समीकरण युग्म

निम्न रैखिक समीकरण युग्म को प्रतिस्थापन विधि से हल कीजिए: - Wired Faculty

Question

निम्न रैखिक समीकरण युग्म को प्रतिस्थापन विधि से हल कीजिए:

$fraction numerator 3 straight x over denominator 2 end fraction space minus space fraction numerator 5 straight y over denominator 3 end fraction space equals space minus space 2$

$straight x over 3 space plus space straight y over 2 space equals space 13 over 6$

Solution

$fraction numerator 3 straight x over denominator 2 end fraction space minus space fraction numerator 5 straight y over denominator 3 end fraction space equals space minus space 2 fraction numerator 9 straight x space minus space 10 straight y over denominator 6 end fraction space equals space minus space 2 rightwards double arrow space 9 straight x space minus space 10 straight y space equals space minus space 12 straight x over 3 space plus space straight y over 2 space equals space 13 over 6 fraction numerator 2 straight x space plus space 3 straight y over denominator 6 end fraction space equals space 13 over 6 rightwards double arrow space 2 straight x space plus space 3 straight y space equals space 13$
9x - 10y = - 12 ...(i)

2x + 3y = 13 ...(ii)
समीकरण (ii) से
$straight x space equals space fraction numerator 13 space plus space 3 straight y over denominator 2 end fraction space space space space space space space space space space space space space space space space space... left parenthesis iii right parenthesis$
x का मान समीकरण (i) में रखने पर
9x - 10y = - 12
$rightwards double arrow space 9 space open parentheses space fraction numerator 13 space plus space 3 y over denominator 2 end fraction space close parentheses space minus space 10 y italic space equals space minus space 12 rightwards double arrow space fraction numerator 9 space left parenthesis space 13 space plus space 3 y italic space right parenthesis space minus space 20 y over denominator 2 end fraction space equals space minus space 12 rightwards double arrow space 117 space plus space 27 y italic space minus space 20 y italic space equals space minus space 24 rightwards double arrow space minus space 47 y italic space equals space minus space 24 space minus space 117 rightwards double arrow space y italic space equals space 141 over 47 space equals space 3$

y का मान समीकरण (iii) में रखने पर

straight x space equals space fraction numerator 13 space minus space 3 straight y over denominator 2 end fraction equals space fraction numerator 13 space minus space 3 space cross times space 3 over denominator 2 end fraction equals space fraction numerator 13 space minus space 9 over denominator 2 end fraction space equals space 4 over 2 space equals space 2

x = 2, y = 3

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