solve the given equation 2x+5y=1;2x+3y=3 by three different methods - graphical method ;substitution method and elimination method
Answers
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
Answer: y=-1 , x=3
Step-by-step explanation:
do it bye substitution method it will be easy 1