Can you explain step by step instructions in solving this problem?

1st you need to remember how to solve a 2-variable/2-equation problem:

2x + 3y = C

4x + 2y = F

You need to eliminate one of the variables. In the above example, you can do this by multiplying each side of the 1st equation by 2

4x + 6y = 2C

4x + 2y = F

and then subtracting the 2nd equation from the first equation:

4y = 2C-F

Solve for y and then plug y into one of the two above equations to solve for x.

For your problem, which is 3 independent equations and 3 variables, the methodology is similar, but you need to eliminate one of your variables in order to reduce your problem to a 2-equation/2-variable one. Example:

x+y+z = G

2x+4y+z = H

3x+8y+3z = I

In this case you can subtract the 1st equation from the 2nd equation to eliminate z to get:

x+3y = H-G

You can then multiply the 2nd equation by 3 and subtract it from the 3rd equation to also eliminate z and get:

-3x-4y = I-H

Now you have two equations and only two variables, x and y. Solve for x and y as discussed above, and then plug these values into one of the 3-variable equations to solve for z.

Combine and cancel. I.E. Figure out how you can combine the equations to cancel terms.

Looking at those equations, I might start by doubling all the terms in the second one. That will give you a 4c term, so if you subtract the whole equation from the first one, the c term will go away.

4m+2c+8d=$5.30. double all terms => 8m +4c +16d = $10.60

Subtract that from 3m + 4c +7d = $5.45

3m - 8m +4c - 4c +8d -16d = $5.45 - $10.60

-5m -8d = -$5.15

Invert it all to clean it up..

5m +8d = $5.15

So you've eliminated one term

Keep going. Try eliminating the c term by combining the second and third equation. Then you'll have 2 equations in m and d, so you can combine them and find m and d. plug m and d back into one of the original equations and you have a full solution for m, c and d.

Do some googling for Gaussian elimination if you want the fully tabular way of solving these sort of systems of equations.

Step1: Label each of the equations Eqn1, Eqn2, and Eqn3, or any other name, to minimize confusion.

Step2: Aim to eliminate one of the variables using two of the three equations.

You might have intermediate equations Eqn4 and Eqn5 in this step.

After this step, you should come up with an equation with only two of the other variables. Label this: Eqn6.

Step3: Aim to eliminate the same variable as in Step2, using another 2 of the original 3 equations.

You might have intermediate equations Eqn7 and Eqn8 in this step.

After this step, you should come up with another equation with only two variables as in Eqn6. Label this: Eqn9.

Step4: Aim to eliminate one of the remaining two variables using Eqn6 and Eqn9.

After this step, you should come up with the value of the last remaining variable.

Step5: Substitute the value of the variable that you've got from Step4 to solve for the value of the other variable in either Eqn4 or Eqn5.

After this step, you should come up with the values of 2 variables.

Step6: Substitute the values of the 2 variables to any of the 3 original equations, then solve for the remaining variable.

Step7: Check the correctness of your answers using any of the 2 other original equations.

Step8: Clearly state your answer.

ILLUSTRATION

Step1

3m+4c+7d=$5.45 Eqn1

4m+2c+8d=$5.30 Eqn2

2m+5c+6d=$5.15 Eqn3

Step2

Aim to eliminate m from Eqn1 and Eqn2:

Multiply 4 to each term in Eqn1

12m + 16c + 28d = 21.80 Eqn4

Multiply -3 to each term in Eqn2

-12m - 6c - 24d = -15.90 Eqn5

Add Eqn5 to Eqn4 to eliminate m

12m + 16c + 28d = 21.80

-12m - 6c - 24d = -15.90

-------------------------------------

10c + 4d = 5.90 Eqn6

Step3

Aim to eliminate m from Eqn2 and Eqn3:

Multiply -1 to each term in Eqn2

-4m - 2c - 8d = -5.30 Eqn7

Multiply 2 to each term in Eqn3

4m + 10c + 12d = 10.30 Eqn8

Add Eqn8 to Eqn7 to eliminate m

-4m - 2c - 8d = -5.30

4m + 10c + 12d = 10.30

-------------------------------------

8c + 4d = 5.00 Eqn9

Step4

Subtract Eqn9 from Eqn6 to eliminate d, then solve for c

10c + 4d = 5.90

8c + 4d = 5.00

----------------------

2c = 0.90

c = 0.45

Step5:

Substitute the value of c to Eqn6, the solve for d:

10c + 4d = 5.90

10(0.45) + 4d = 5.90

4.50 + 4d = 5.90

4d = 5.90 - 4.50

4d = 1.40

d = 0.35

Step6

Substitute the values of c and d to Eqn1, then solve for m

3m + 4c+ 7d = 5.45

3m + 4(0.45)+ 7(0.35) = 5.45

3m + 1.80 + 2.45 = 5.45

3m = 5.45 - 1.80 - 2.45

3m = 1.20

m = 0.40

Step7

Check using Eqn2:

4m + 2c + 8d = 5.30

4(0.40) + 2(0.45) + 8(0.35) = 5.30

1.60 + 0.90 + 2.80 = 5.30

5.30 = 5.30 Yes!

Checking using Eqn3 should yield the same result.

Step8

Answer: m = 0.40, c = 0.45, d = 0.35.

once you've become good at these questions your ready to tackle IVP problems !! =].

but the traditional way to solving these kind of problems is to eliminate one of those variables and work backwards once you've found the value for one.