Question

$f(x) = 2h + \frac{k}{2} = 17$
$f(x) = 3h + \frac{k}{3} = 23$
find the value of h and k​

Answer 1

Answer:

h = 7, k = 6

Step-by-step explanation:

Solving 2 simultaneous equations

2h + $\frac{k}{2}$ = 17 ← multiply through by 2 to clear the fraction

4h + k = 34 → (1)

3h + $\frac{k}{3}$ = 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