SOLUTION: How do you know what to use to solve linear systems of equations? I've been doing problems online and they say what to use (addition, subtraction, make the left sides equal to each

Question 877415: How do you know what to use to solve linear systems of equations? I've been doing problems online and they say what to use (addition, subtraction, make the left sides equal to each other etc.) but I haven't seen anything about why each way works for each problem.
For example:
Create a new equation by setting the left-hand sides of the equations equal to each other. y = 2x - 1 and 2y + x = 3.
How would you know that you can solve this, by making the left sides equal to each other (y = 2y + x), without being told to solve it that way?
Create a new equation by setting the left-hand side of the first equation equal to the right-hand side of the second equation. 2y = 2/5x - 3 and -24 = 4x + y.
How would you know that you can solve this by setting the left side of the first = to the right side of the second (2y = 4x + y)?
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
Maybe you are studying from the wrong source. Use a good Algebra 1 or Introductory Algebra textbook, and stop relying on something you find online. Good Algebra textbooks will develop the properties of numbers and the skills to use, and following those in the sequence presented in the books will give you much better, clearer development.

The techniques you use are all basically forms of substitution. In a linear system of equations with a solution, substitution works, because two expressions or numbers are stated as equal; so you can use either expression in any of the equations of the system.

Everything will make sense, if you study carefully and thoroughly from a good source of instruction.

Create a new equation by setting the left-hand sides of the equations equal to each other. y = 2x - 1 and 2y + x = 3.
Is this to solve the system?
Work first with the second equation----

, meaning y has two expressions which are found to be equal.
-
, first equation
, second equation now transformed
Both expressions equal to y:
----Solve this for x.
.
.
You know what to do for this one?
RELATED QUESTIONS
Solving Systems of Linear Equations by Graphing 2x-y=4 x+y=5 How do I do these... (answered by checkley77)

I am not sure if I know what I am doing, I am taking an online algebra class. I am... (answered by jim_thompson5910)

How can i use linear equations to solve problems (answered by addingup)

I am doing systems of linear equations. I know how to do the equation until I get an... (answered by harihara)

the question is solve for J. Q=I^2Rt/J This whole concept of literal equations has (answered by Fombitz,rapaljer)

I have been studying all day and doing practice problems from my math book to get me... (answered by Jeef Gorrdon,richwmiller)

When solving a system of equations, how do I know what numbers to put in place of x and... (answered by jim_thompson5910)

in solving systems of linear equations how do you know whether to eliminate the x's or... (answered by bucky)

I'm solving equations with variables on both sides. I don't know what the last question... (answered by stanbon)