4h + 3c = 23.75 6h + 2c = 25

Answer 1

To solve this system of equations, we can use the method of substitution or elimination.

Let's solve it using the substitution method:

From the first equation, we can solve for h in terms of c:

4h + 3c = 23.75
4h = 23.75 - 3c
h = (23.75 - 3c) / 4

Now plug this expression for h into the second equation:

6[(23.75 - 3c) / 4] + 2c = 25
(142.5 - 18c) / 4 + 2c = 25
142.5 - 18c + 8c = 100
-10c = -42.5
c = 4.25

Now that we have the value of c, we can substitute it back into the equation for h:

h = (23.75 - 3*4.25) / 4
h = (23.75 - 12.75) / 4
h = 11 / 4
h = 2.75

Therefore, the solutions to this system of equations are h = 2.75 and c = 4.25.