Answer:
d = (c -4)² +7 = c² -8c +23
Step-by-step explanation:
Both 'c' and 'd' are expressed in terms of the variable k. In general, that variable is eliminated by writing k in terms of 'c' or 'd', then substituting for k in the other equation.
Eliminating k
We recognize that the 9k² term in the expression for 'd' is the square of the 3k term in the expression for 'c'. That means we don't have to solve for k; we only need to solve for 3k. The equation for 'c' gives an easy way to do that.
c = 3k +4
c -4 = 3k . . . . . . . subtract 4 to get an expression for 3k
Substituting into the equation for 'd', we have ...
d =7 +9k²
d = 7 +(3k)² . . . . . writing 9k² in terms of 3k
d = 7 +(c -4)² . . . . substituting for 3k. This is d in terms of c.
This can be simplified to ...
d = c² -8c +23 . . . . another form of d in terms of c.
