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

Interval notation, I can find what x means I just cant do the interval nota...

I can find what x means I just cant do the interval notation correctly

Test prep, 1). Using the function: y=y0,(.90)^t-1. In this equation y0 is t...

1). Using the function: y=y0,(.90)^t-1. In this equation y0 is the amount of initial dose and y is the amount of medication still available t hours after drug is administered. Supp

Polynomial inequalities, Now it is time to look at solving some more hard i...

Now it is time to look at solving some more hard inequalities.  In this section we will be solving (single) inequalities which involve polynomials of degree at least two.  Or, to p

Sketch the graph of the common logarithm, Example Sketch the graph of the ...

Example Sketch the graph of the common logarithm & the natural logarithm on the similar axis system. Solution This instance has two points.  Firstly, it will familiarize u

Linear equation in two variables, 2x+y/x+3y=-1/7and 7x+36y=47/3 hence find ...

2x+y/x+3y=-1/7and 7x+36y=47/3 hence find p if xy=p=x/y

Quadratic function to vertex form, write the following function x^2-2x-1 in...

write the following function x^2-2x-1 in the form of y=a(x-h)^2+k

Standard form, 4(x)^2-40x+107 in standard form

4(x)^2-40x+107 in standard form

Equivalent Ratios and Graphs, A car travels at a rate of 50 miles per hour....

A car travels at a rate of 50 miles per hour.Use equivalent ratios to graph the distance the car travels over time.Graph time on the x-axis and distance on the y-axis

Unitary method, What are the pre conditions to applying unitary method to a...

What are the pre conditions to applying unitary method to a given problem? e.g. We know that 37 degrees celsius is equal to 98.6 degrees fahrenheit, but 1 degrees celsius is not eq

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