How do I solve these by either substitution/ elimination? I'd also like to know how to solve them using matrices.
I need to find the values of the constants a, b, c are.
Gotcha. Well you can use substitution here but it's tricky and a lot of algebra. If you want to use matrices like you said, first write out three equations. Make sure they are all in the same form, meaning the a's, b's and c's line up. Then make a 3x3 matrix of the left hand side of these three equations. Make another matrix that is 3x1 matrix of the right hand side of the three equations. If the first one is A and the second one is B, then take and you'll get a 3x1 matrix as your answer which is the solution for a,b and c.
Normally calculator's are allowed for this method.
Anyway, if you want to do it by hand, it's just like with two variables. Solve an equation for one variable in terms of the others. You can do this a couple times and get two equations with two unknowns. Solve them normally then use that to find the 3rd solution.
None of this makes any sense to me. See the red.
Do you mean the following?:
4 = a + b + c .... (1)
10 = 4a + 2b + c .... (2)
18 = 9a + 3b + c .... (3)
The following will give you two equation in a and b:
Equation (2) - equation (1):
Equation (3) - equation (1):
Solve them for a and b. Then use those values in one of the equations to solve for c.