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

Geometric Sequences, How do you write an exponential decay function to mode...

How do you write an exponential decay function to model a situation?

Geometry, The length of a rectangle is twice it''s width. If the length of ...

The length of a rectangle is twice it''s width. If the length of its diagonal is 16root5 cm, find its area

Test , linear functions

linear functions

Product using identities, i want to find the product using suitaible identi...

i want to find the product using suitaible identities: (x+y+2z){(x*x)+(y*y)+4(z*z)-xy-2yz-2zx}

Equivalent values, two debts- the first of 800 is due six month ago and the...

two debts- the first of 800 is due six month ago and the second of 1400 borrowed one year ago for a term of three years at 6.5% compunded annulallu are to be replaced by a single p

Perimeter, a farmer has a garden with 2 sides at right angles and the third...

a farmer has a garden with 2 sides at right angles and the third side is 423ft.long.find the perimeter of the garden. if the angle between the shortest and the longest side is 58''

Equations, 2(5+6csquared)-30divided by 3 c=2 d=4

2(5+6csquared)-30divided by 3 c=2 d=4

Rational expressions, I am looking the domain of g^2-6g-55/g. The denominat...

I am looking the domain of g^2-6g-55/g. The denominator here can be also be written as 1g, right?

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