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 ___________ __

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

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)   (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)   (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.

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

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

Learn the subject from there.

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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

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