Question

3x=7y-21, If (0, a) and (b, 0) are the solutions of the given linear equation. Find ‘a’ and ‘b’.

Answer 1

Hey there !!!

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===>>>>> Solution

Let first write the given equation in its general form.

ax + by = c .......( linear equation)

Given equation,

3x = 7y - 21

3x - 7y = -21 ..........(general form )

Now, it is given that ...

(0,a) and (b,0) are the solutions of the given equation.


Case (I)
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Compare (0,a) with (x,y) hence the value we obtained are ,

x = 0. and y = a

Now,put this values in the given equation we get,

3x - 7y = -21

3*0 - 7*a = -21

0 - 7a = -21

a = -21/-7

a = 3

∴[ a = 3 ]


Case (II)
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Now, compare (b,0) with (x,y) hence the value we obtained are ,

x = b and y = 0

Now, put this value in the given equation we get,

3x - 7y = -21

3*b - 7*0 = -21

3b - 0 = -21

b = -21/3

b = -7

∴ [ b = -7 ]

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Let check whether our answer is correct or not .

we know that,

(0,a) and (b, 0) are the solution of the given equation ,

(0,a) = (x,y) = (0,3)

(b,0) = (x,y) = (-7, 0)

1.) Put x = 0 and y = 3 in the given equation

3x - 7y = -21

3*0 - 7*3 = -21

0 -21 = -21

-21 = -21

L.H.S = R.H.S


2.) Put x = -7 and y = 0 in the given equation ,

3x - 7y = -21

3*(-7) - 7*0 = -21

-21 - 0 = -21

-21 = -21

L.H.S = R.H.S

Proved
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✴✴✴✴✴✴✴✴✴R.N.S✴✴✴✴✴✴

Answer 2

It is given that ,

( 0 , a ) and ( b , 0 ) are solutions of

3x = 7y - 21 .

i ) Substitute ( 0 , a ) in the equation,

3 × 0 = 7 × a - 21

=> 0 = 7a - 21

=> -7a = -21

=> a = ( -21 )/( -7 )

Therefore ,

a = 3

ii ) Substitute ( b , 0 ) in the equation ,

3× b = 7 × 0 - 21

=> 3b = -21

=> b = ( -21 )/3

Therefore

b = -7

Therefore ,

a = 3 and b = -7

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