Question

Find a and b if the points p(6,0) and q(3,2) lie on the graph of ax + by =12

Answer 1

`a= 2`

`b = 3`

Explanation:

Given

`p(x,y) = (6,0)`

`q(x,y) = (3,2)`

`ax + by = 12`

Required

Find a and b

In
`p(x,y) = (6,0)`,
`x = 6` and
`y = 0.`

This gives:

`a*6 + b*0 = 12`

`6a = 12`

Divide by 6

`a= 2`

In
`q(x,y) = (3,2)`.
`x = 3` and
`y = 2.`

This gives:

`a*3 + b*2 = 12`

`3a + 2b = 12`

Substitute 2 for a

`3*2 + 2b = 12`

`6 + 2b = 12`

Collect Like Terms

`2b = 12 - 6`

`2b = 6`

Divide by 2

`b = 3`