Inconsistent systems example, Algebra

Inconsistent systems example

Example Solve the given systems of equations.

x - y = 6

-2x + 2 y = 1

Solution

We can utilize either method here, although it looks like substitution would possibly be slightly easier.

We'll solve out the first equation for x & substitute that in the second equation.

x = 6 + y

-2 (6 + y )+ 2 y = 1

-12 - 2 y + 2 y = 1

-12 =1  ??

Thus, this is clearly not true and there doesn't seem to be a mistake anywhere in our work.  Hence, what's the problem?  To see let's graph these two lines and illustrates what we get.

357_Inconsistent systems example.png

It seem that these two lines are parallel (can you check that with the slopes?) and we know that two parallel lines along with different y-intercepts (that's significant) will never cross.

Since we saw in the opening discussion of this section solutions revel the point where two lines intersect.  If two lines don't intersect we can't comprise a solution.

Thus, when we get this kind of nonsensical answer from our work we contain two parallel lines and there is no solution to this system of equations.

This system is called inconsistent.  Note that if we'd utilized elimination on this system we would have ended up with a similar nonsensical answer.

Posted Date: 4/8/2013 5:23:26 AM | Location : United States







Related Discussions:- Inconsistent systems example, Assignment Help, Ask Question on Inconsistent systems example, Get Answer, Expert's Help, Inconsistent systems example Discussions

Write discussion on Inconsistent systems example
Your posts are moderated
Related Questions
To find the calorie density (D) in calories per ounce of food that contains c carories and weight w ounces is given by D=C/w

http://www.transtutors.com/live-online-tutor/math-help/

Definition of an exponential function If b is any number like that b = 0 and b ≠ 1 then an exponential function is function in the form,

Hi everyone, needing help with these math questions. Please include your workings out so I can understand how you got your answers,thanks! INTRO: Three friends have been training

How do i do an fx problem?


By using transformations sketch the graph of the given functions.                        g ( x ) = x 2 + 3 Solution Here the first thing to do is graph the function wit


What are the different ways to multiply/add/subtract/divide and work with square roots?

We now can also combine the two shifts we only got done looking at into single problem.  If we know the graph of f ( x ) the graph of g ( x ) = f ( x + c ) + k will be the graph of