Question

when the point ( k, 3 ) lies on each of these lines, find the value of k y= 3x+1 , y= 4x-2 , y=1/2x - 1 and 2x+3y=4

Answer 1

see explanation

Explanation:

Since (k, 3) lies on each of the lines, the point satisfies the equations.

Substitute x = k, y = 3 into each and solve for k

y = 3x + 1

3 = 3k + 1 ( subtract 1 from both sides )

2 = 3k ( divide both sides by 3 )

k =
`(2)/(3)`

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y = 4x - 2

3 = 4k - 2 ( add 2 to both sides )

5 = 4k ( divide both sides by 4 )

k =
`(5)/(4)`

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y =
`(1)/(2)` x

3 =
`(1)/(2)` k ( multiply both sides by 2 to clear the fraction )

k = 6

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2x + 3y = 4

2k + 3(3) = 4

2k + 9 = 4 ( subtract 9 from both sides )

2k = - 5 ( divide both sides by 2 )

k = -
`(5)/(2)`