SOLUTION: Write an equation that can form a linear system of equations with -2x + y = 4 so that the system has: a) no solution ___________ ___ b) many solutions ___________ ___ c) one sol

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Write an equation that can form a linear system of equations with -2x + y = 4 so that the system has: a) no solution ___________ ___ b) many solutions ___________ ___ c) one sol      Log On


   



Question 1204363: Write an equation that can form a linear system of equations with -2x + y = 4 so that the system has:
a) no solution _______________
b) many solutions _______________
c) one solution _______________

Found 2 solutions by mananth, ikleyn:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!

Write an equation that can form a linear system of equations with -2x + y = 4 so that the system has:
Parallel lines have no solutions. slopes are equal
a) no solution -2x +y=10

Both equations in the system represent the same line on graph .

b) many solutions : -6x+3y= 30

The lines intersect each other .
c) one solution : 2x+y =10




Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.

The answer to  (b)  in the post by  @mananth is incorrect.

As it is written in his answer to  (b),  that system of equations  DOES  NOT  have solutions.



A correct answer to  (b)  (one of many others)  is   -6x+3y= 12.

Then the system really has many solutions.

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

Learn the subject from there.