If the solution of ax + 3y = 8 and 2x + by = 10 is (3, 4) what are a and b.

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The solution of the system of linear equations ax + 3y = 8 and 2x + by = 10 is (3, 4). An easy way to determine the values of a and b is to use the fact that as the two lines intersect at (3, 4) this point lies on both the lines.

Substitute x = 3 and y = 4 in ax + 3y = 8

=> 3a + 12 = 8

=> 3a = -4

=> a = -4/3

Substitute x = 3 and y = 4 in 2x + by = 10

=> 6 + 4b = 10

=> 4b = 4

=> b = 1

The required values of a and b are -4/3 and 1 respectively

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