Lesson HOW MANY SOLUTIONS can there be in a linear equation?

Algebra ->  Algebra  -> Coordinate Systems and Linear Equations -> Lesson HOW MANY SOLUTIONS can there be in a linear equation?      Log On

Ad: You enter your algebra equation or inequality - Algebrator solves it step-by-step while providing clear explanations. Free on-line demo .
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

   

This Lesson (HOW MANY SOLUTIONS can there be in a linear equation?) was created by by ichudov(404) About Me : View Source, Show
About ichudov: I am not a paid tutor, I am the owner of this web site.
How many solutions can there be in a linear equation , where c, b, and c are constants?

The first answer that leaps to mind is one solution. Usually, especially in regular school math, that is the case. But not always.

Case 1. One Solution


All linear equations ax+b=c where a is not equal to zero, have one solution:

Case 2. No Solutions


A linear equation can have no solutions. Example: 0x + 1 = 2. Since 0x is always 0, and 0+1 = 1, we have an impossible equation 1=2. Any linear equation with no solution always has zero (0) as the coefficient before x.

Case 3. Infinitely many solutions


A linear equation can have infinitely many solutions. Example: 0x+4=4. Since 0x is always 0 regardless of x, any value of x satisfies this equation.

Conclusions


So, be careful with problems that reduce to a linear equation. Beware that they may have no solutions or an infinite number of solutions.
This lesson has been accessed 4808 times.