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Question
If the point of intersection of ax + by = 7 and bx + ay = 5 is (3,1), then find the value of a and b.
Solution
ax + by = 7 and bx + ay = 5
The point of intersection lies on both the equations
It will satisfy the given equation
ax + by = 7
put x = 3 and y = 1
3a + b = 7 ................. (1)
bx + ay = 5 [Given]
put x = 3 and y = 1
`therefore` 3b + a = 5 .................. (2)
Adding equation (1) and (2)
3a + b = 7
a + 3b = 5
____________________
4a + 4b = 12
`therefore` 4 (a - b) = 12
`therefore a + b = 12/4`
a + b = 3 ....(3)
Suntracting equation (1) and (2)
3a + b = 7
a + 3b = 5
________________
2a - 2b = 2
2 (a - b) = 2
a - b = `2/2`
a - b = 1 ....(4)
Adding equation (3) and (4)
a + b = 3
a - b = 1
____________
2a = 4
a = `4/2`
a = 2
Substituting a = 2 in equation (3)
3a + b = 7
3(2) + b = 7
6 + b = 7
b = 7 - 6
b = 1
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