Question

(3,4) is the point of intersection of the lines ax+by=18 and bx +ay= 17 . what are the values of a and b?​

Answer 1

Solution:-

ax + by = 18 .....(i) eq

bx + ay = 17 .....(ii) eq

( 3 , 4 ) is the point of intersection:- x = 3 and y = 4

Its Satisfied the :- ax + by = 18

We get ,

3a + 4b = 18 .........(i)eq

( 3 , 4 ) is the point of intersection:- x = 3 and y = 4

Its satisfied the bx + ay = 17

We get ,

3b + 4a = 17 .......(ii) eq

Now we have two equation and two unknown value

Using elmination methods

By subtracting, We get

3a + 4b = 18 .....(i) × 4

4a + 3b = 17 .....(ii) × 3

=> 12a + 16b = 72

12a + 9b = 51

- - -

0 + 7b = 21

=> b = 21 / 7

b = 3

Now put the value b on (i) st equation, we get

=> 3a + 4b = 18

=> 3a + 4 × 3 = 18

=> 3a + 12 = 18

=> 3a = 18 - 12

=> 3a = 6

=> a = 6 / 3

=> a = 2

Value of a = 2 and b = 3

Answer 2

Given ,

(3,4) is the point of intersection of the lines

• ax + by = 18 and bx + ay = 17

Thus , put x = 3 and y = 4 , we get

3a + 4b = 18 --- (i)

3b + 4a = 17 --- (ii)

Multiply eq (i) by 4 and eq (ii) by 3 , we get

12a + 16b = 72 --- (iii)

9b + 12a = 51 --- (iv)

Subtract eq (iv) from eq (iii) , we get

12a + 16b - (9b + 12a) = 72 - 51

7b = 21

b = 21/7

b = 3

Put b = 3 in eq is (i) , we get

3a + 4(3) = 18

3a + 12 = 18

3a = 6

a = 6/3

a = 2

$\sf{ \therefore \underline{ The \: value \: of \: a \: and \: b \: are \: 2 \: and \: 3}}$