how do you solve for all of the variables using system of equations

Question

2a-3b=-5, 4a+3b=17, 5c-2a=1

Answer 1

There are three equations in three variables. That means that we can solve for the three variables.

In later math, you will use matrix operations to perform similar steps. For now, you must go through steps to simplify the problem by making TWO equations in TWO variables that you may solve either by substitution or by elimination.

So, to start, you combine two of the equations to form ONE equation in TWO variables. You may use either substitution or elimination to do that.

If the system is: 2a-3b=-5, 4a+3b=17, 5c-2a=1

You may add the first two equations to eliminate the b term and get 6a=12, So, a=2. Then substitute into the third equation to get c=1.

Note that each system is different and is solved differently, but with the same strategy.

Answer 2

I would use elimination on the first two equations since they use the same two variables, then substitute that solution into the third equation and first equation.

Answer 3

By using either elimination or substitution.

Do you have a question as to how these are done?