Question

`f(x) = 2h + (k)/(2) = 17`


`f(x) = 3h + (k)/(3) = 23`
find the value of h and k​

Answer 1

h = 7, k = 6

Explanation:

Solving 2 simultaneous equations

2h +
`(k)/(2)` = 17 ← multiply through by 2 to clear the fraction

4h + k = 34 → (1)

3h +
`(k)/(3)` = 23 ← multiply through by 3 to clear the fraction

9h + k = 69 → (2)

Subtract (1) from (2) term by term to eliminate k

(9h - 4h) + (k - k) = (69 - 34), that is

5h = 35 ( divide both sides by 5 )

h = 7

Substitute h = 7 in either of the 2 equations for corresponding value of k

Substituting h = 7 in (1)

4(7) + k = 34

28 + k = 34 ( subtract 28 from both sides )

k = 6