How do I find the value of a letter in algebra? if it doesn't come with the result.

Question

For example, my math problem comes like:

a + 4b - 3c

How do I solve this? How do I know what the letters' value is? It's so confusing, and I can't get any help online or so, and it's not possible for me to ask anyone, so I'm really hoping I can find an answer here!

Answer 1

a + 4b - c without more information doesn't allow for solving the value of any of the letters.

If a+4b -c = 0

then you can solve for each letter, in terms of the other two letters

a= c-4b

c = a+4b

b=(c-a)/4

If you had 3 equations, you could solve for unique numerical values of each letter, unless the equations were linearly dependent, or contradictory.

if a+4b -c = 0

and a 2nd equation were a+4b -c = 1,

then the system of equations has no solution, as they're contradictory

if 3 equations, 3 unknowns were linearly dependent, such as

a+4b -c = 0

2a +8b -2c = 0

3a +12b -3c = 0

are just multiples of each other and that means an infinite number of solutions for a,b and c

if 3 equations, 3 unknowns are linearly independent (not multiples of each other) and not contradictory, then there is a unique (one) solution for a, b and c

such as

a + 4b - c = 0

a+4b = 2

a-c = 4

then

a = 6, b=-1, c=2 is the one and only solution

if you graphed the equations in 3 dimensions, they would intersect at that point (a,b,c) = (6,-1,2)