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solve the given equation 2x+5y=1;2x+3y=3 by three different methods - graphical method ;substitution method and elimination method |
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Answer» Given Equation ⇒2x + 5y = 1 (i)eq ⇒2x + 3y = 3 (ii)eq METHOD:- 1 Graphical method Take Eq(i) 2x + 5y = 1 When X =0 ⇒2×0 +5y =1 ⇒5y = 1 ⇒y=1/5 When y = 0 ⇒2x + 5×0 = 1 ⇒2x =1 ⇒x = 1/2 point is (1/5 , 1/2) Take Eq(ii) 2x + 3y = 3 When y = 0 ⇒2x + 3×0 =3 ⇒2x = 3 ⇒x=3/2 When x = 0 ⇒2×0 + 3y = 3 ⇒y = 3/3 = 1 method:-2 Substitution Method ⇒2x + 5y = 1 (i)eq ⇒2x + 3y = 3 (ii)eq Take 2x + 5y = 1 (i)eq ⇒2x + 5y = 1 ⇒2x = 1 - 5y (iii)eq PUT the value of 2x on (ii)eq ⇒2x + 3y = 3 (ii)eq ⇒1 - 5y + 3y = 3 ⇒1 - 2y = 3 ⇒1 - 3 = 2y ⇒-2 = 2y ⇒-2 = 2y ⇒y = -1 Now put the value of y on (iii) eq ⇒2x = 1 - 5y ⇒2x = 1 + 5 ⇒2x = 6 ⇒x = 3 So x = 3 and y = -1 Method:-3 ELIMINATION method ⇒2x + 5y = 1 (i)eq ⇒2x + 3y = 3 (ii)eq Subtract (ii) from (i) ⇒2x + 5y - ( 2x + 3y ) = 1 - 3 ⇒2x + 5y - 2x -3y = -2 ⇒2y = -2 ⇒y = -1 Put the value of y on (i)eq ⇒2x + 5y = 1 (i)eq ⇒2x + 5(-1) = 1 ⇒2x - 5 = 1 ⇒2x = 6 ⇒x =3 so x = 3 and y = -1
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