Inconsistent systems example, Algebra

Assignment Help:

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.


Related Discussions:- Inconsistent systems example

Polynomials, please help me understand polynomials- i get the small problem...

please help me understand polynomials- i get the small problems but i dont understand larger ones

Rational Expressions, I''m having trouble with this problem..t squared-16 d...

I''m having trouble with this problem..t squared-16 divided by t squared minus-t-20

Pre-algebra, what is the price per gallon, if it cost 61.80 to fill a 15-ga...

what is the price per gallon, if it cost 61.80 to fill a 15-gallon tank?

Polynomial satisfy - rational root theorem, Example: prove that the roots ...

Example: prove that the roots of the below given polynomial satisfy the rational root theorem. P ( x ) = 12x 3 - 41x 2 - 38x + 40 = ( x - 4) (3x - 2) ( 4x +5) Solution

Help..., I am a 14 year old 9th grade Freshmen, I seriously need help. I am...

I am a 14 year old 9th grade Freshmen, I seriously need help. I am failing with a 49.00 grade in my class

Fractions, how do you solve a different fractions

how do you solve a different fractions

Graphing polynomials, In this section we are going to look at a technique f...

In this section we are going to look at a technique for getting a violent sketch of a general polynomial. The only real information which we're going to required is a complete list

Bear population a word problem, To estimate the size of the bear population...

To estimate the size of the bear population in Keweenaw Pennisula, conservationists captured, tagged and released 50 bears. One year later, a random sample of 100 bears included on

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd