Question 877415
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.


<i>Create a new equation by setting the left-hand sides of the equations equal to each other. y = 2x - 1 and 2y + x = 3. </i>
Is this to solve the system?
Work first with the second equation----
{{{2y+x=3}}}
{{{2y+x-x=3-x}}}
{{{2y=3-x}}}
{{{2y(1/2)=(3-x)(1/2)}}}
{{{y=(3-x)/2}}}, meaning y has two expressions which are found to be equal.
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{{{y=2x-1}}}, first equation
{{{y=(3-x)/2}}}, second equation now transformed 
Both expressions equal to y:
{{{2x-1=(3-x)/2}}}----Solve this for x.
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You know what to do for this one?