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:

$square root of 2 space straight x end root space plus space square root of 3 space straight y end root space equals space 0 square root of 3 space straight x end root space minus space square root of 8 space straight y end root space equals space 0$

Solution

square root of 2 space straight x end root space plus space square root of 3 space straight y end root space equals space 0 space space space space space space space space space space space space space space space space.... left parenthesis straight i right parenthesis square root of 3 space straight x end root space minus space square root of 8 space straight y end root space equals space 0 space space space space space space space space space space space space space space space.... left parenthesis ii right parenthesis

समीकरण (ii) से

square root of 3 space straight x end root space equals space square root of 8 space straight y end root rightwards double arrow space straight x space equals space fraction numerator square root of 8 over denominator square root of 3 space straight y end fraction space space space space space space space space space space space.... left parenthesis iii right parenthesis

t का मान समीकरण (i) में रखने पर

square root of 2. space fraction numerator square root of 8 over denominator square root of 3 end fraction space straight y space plus space square root of 3 space straight y space equals space 0 rightwards double arrow space fraction numerator 4 over denominator square root of 3 end fraction space straight y space plus space square root of 3 space straight y end root space equals space 0 rightwards double arrow space open parentheses space fraction numerator 4 over denominator square root of 3 end fraction space plus space square root of 3 space close parentheses space straight y space equals space 0 rightwards double arrow space straight y space equals space 0

y का मान समीकरण (iii) में रखने पर

straight x space equals space fraction numerator square root of 8 over denominator square root of 3 end fraction space left parenthesis space 0 space right parenthesis space equals space 0

x = 0, y = 0