Question

Find the value to a and



b.If the line 2ax +3by=18 and 5ax +3by = 15 passes through (1,1)

Answer 1

2ax + 3by = 18

⇒ At (1 , 1 ), 2a + 3b = 18

5ax +3by = 15

⇒ At (1, 1) , 5a + 3b = 15

Put the two equations together:

2a + 3b = 18 ------------------- [ 1 ]

5a + 3b = 15 ------------------- [ 2 ]

FInd a:

[ 1 ] - [ 2 ]:

-3a = 3

a = -1  ------------------- Sub into equation [ 1 ]

Find b:

2a + 3b = 18

2( -1 ) + 3b = 18

-2 + 3b = 18

3b = 20

b = 20/3

Answer; a = - 1 and b = 20/3

Answer 2

Solution:

If both the lines passes through (1,1) that means the point lie on both the lines

just put the value x = 1 and y = 1 in the lines

1)
$2a(1) + 3b(1) = 18 \\ \\ 2a + 3b = 18 \: \: \: \: ........eq1$
2)

$5a(1) + 3b(1) = 15 \\ \\ 5a + 3b = 15 \: \: \: \: \: ......eq2$
Now, subtract both the equation

$2a + 3b - 5a - 3b = 18 - 15 \\ \\ - 3a = 3 \\ \\ a = - 1$
put a= -1 in eq1

$2( - 1) + 3b = 18 \\ \\ 3b = 20 \\ \\ b = 6.66$
So , a = -1 , b= 6.66 is the final answer