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Solve the following linear systems. For each system, is thereno solution, a unique solution, or infinitely many solutions? ....

Question

Solve the following linear systems. For each system, is thereno solution, a unique solution, or infinitely many solutions? .

solve the following linear systems. For each system, is there no solution, a unique solution, or infinitely many solutions? .



Answers

What is the solution of a system of linear equations?

Hello students in here. We have to discuss about this solution off the system. Off questions Soil right here, a solution off system off equations. So let's see what it is. So let's suppose that we have a system off the question that is even next plus B one y is equal to see when this is your first question. So a two x plus b two way is equal to see to. This is our second question. So let's discuss what, what the solution off this will be. So if you look at our first question in the system off a question, this is a one x plus b one y plus. Even this is nothing but an equation off straight line, right? So let's suppose that this is our straight line for the question one. And if you look at the second question, this is also a straight line, a question that is a two x plus buta way. Is it going to see toe? So let's suppose that this is our second questions that this is the line second light second questions line. Now, if you look at the point of intersection is a unique point, right Let's suppose that dis coordinated X com away. Now if this if you have to solve if we have to find the solution of this to your question, we'll look for the point of intersection of these two lines if we get if we somehow get the unique point of intersection of these two, these two lines, if you get the unique point of intersection of these two lines, will get a unique solution for X com away, right? We'll get a unique coordinate for X Come away, and this will be the solution of this equation. If somehow we're not getting any of the point. Let's suppose that the lines that peddler one case, maybe the lines are parallel this line year and this land pellets of you will not get any of the point of intersection of these two land. So in that case, we'll have no solution, right? No solution. Now, one cases also there that these two lines are representing the These three questions are representing the same line. So in that case, these two lines are represented sort of. These three questions are representing the same lines, so in that case, we'll have in final solutions. So we have three possible for use cases for the solution of system off questions. It can be a unique solution. X com away If the line represented by the questions are intersecting to each other, this is the point of intersection. Now this can be having no solutions if the lions representing why the question is, are my leg to each other. And this can have also in financially many solutions. If the line representing where these two questions are this same is the same line. So hope you understood the video and thanks for watching.

A solution set to a system of linear equations is the set of all points that the two lines have in common. You can have a solution set with one point. You can have a solution set with Internet number of points, or you can have no solution.

A system of equations with one solution could be Why equals three X plus four and why equals negative two X minus seven Hear what I need to look for are different. Slows a system of equations with infinite solutions. Could be why equals to s plus Southern and to why equals four X plus 14 If you notice I multiplied the first equation by two simplifying it. I would take out that common factor of two, which would bring us back to Why equals two x plus seven. So here what I did any solution with equal slows and equal, why intercepts? We'll have infinite solutions. An example of no solution could be Why equals two X plus four and why equals two X minus seven For a system toe have no solution. We would have equal slopes, but difference why intercepts?

In this family have a picture, and we want to see how many solutions are. And we can see that when you look at the intersection of these three planes, it doesn't just intersect. At one point, it intersects the line. So if you think about where the three intersect, there will be a line of all solutions insistence. It's not just one point, it's online. It confuse any point on this line as a solution. Insistence the Linus infinitely lying. And it's infinitely number of points you can pick on this line. The number of solutions is going to be infinite.


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