SOLUTION: Solve the linear systems using any method of your choice. 2x-y=1 4x-2y=2

Algebra.Com
Question 1177923: Solve the linear systems using any method of your choice.
2x-y=1
4x-2y=2
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!


.........both divide by
--------------------


---------------------------
=> These two lines are exactly the same line. Therefore, the given system of equation has infinitely many solutions.
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.

Consider the extended matrix. 


It is easy to see that its rows are proportional.



It means that one equation is equivalent to the other equation,

so FACTUALLY you have only one equation in two unknowns.



Such system has INFINITELY MANY solutions.


Take x as a FREE variable and express  y = 2x-1  from the first equation.


You may give any value to x and calculate the respective value of y: each such a pair (x,y) will be a solution.

Solved and explained.

-------------

See the lesson
    - Geometric interpretation of the linear system of two equations in two unknowns
in this site.



RELATED QUESTIONS

Solve the linear systems using any method of your choice. y=2-3x... (answered by MathLover1)
Solve the following systems of equations using a method of your choice. 6x-y=-4... (answered by Alan3354)
solve the system using your choice of method: 3x^2-2y^2=1... (answered by orca)
solve using any method of your choice: a. 1/2x - 1/8y= -1/4 4x-y=-2 b. x=5y... (answered by Alan3354)
what is the solution? Solve the systems of linear equations using a graphing method... (answered by checkley77)
Solve the following systems of linear equation by using Substitution Method: 1,) X +3y (answered by josgarithmetic)
can i have help solving Solve the systems of linear equations using a graphing method (answered by solver91311)
Solve the system of linear equations using your method of choice. 2x − y + 3z=13 (answered by Alan3354)
Solve the system of linear equations using any method. 2x + y = 5 and 4x + 3y = 11 (answered by mananth)