answersLogoWhite

0

So, take the case of two parallel lines, there is no solution at all. Now look at two equations that represent the same line, they have an infinite number of solutions. The solution is unique if and only if there is a single point of intersection. That point is the solution.

User Avatar

Wiki User

15y ago

Still curious? Ask our experts.

Chat with our AI personalities

EzraEzra
Faith is not about having all the answers, but learning to ask the right questions.
Chat with Ezra
TaigaTaiga
Every great hero faces trials, and you—yes, YOU—are no exception!
Chat with Taiga
RafaRafa
There's no fun in playing it safe. Why not try something a little unhinged?
Chat with Rafa

Add your answer:

Earn +20 pts
Q: Does every pair of linear simultaneous equations have a unique solution?
Write your answer...
Submit
Still have questions?
magnify glass
imp
Continue Learning about Math & Arithmetic

When does a system of linear equations in two variables have a unique or one solution?

simultaneous equations


What does a air of linear equations having a unique solution represent graphically?

Presumably the question concerned a PAIR of linear equations! The answer is two straight lines intersecting at the point whose coordinates are the unique solution.


When will be the linear equations a1x plus b1y plus c1 equals 0 and a2x plus b2y plus c2 equals 0 has unique solution?

When (the graph of the equations) the two lines intersect. The equations will tell you what the slopes of the lines are, just look at them. If they are different, then the equations have a unique solution..


Is there simultaneous equation which cant be solved?

By definition, there cannot be a simultaneous equation that cannot be solved, there must be a set of simultaneous equations. It is important to realise that simultaneous equations need not be linear.It is simple to devise a pair of linear equations that are inconsistent:x + y = 1 and x + y = 2There is no solution. Graphically, the two lines are parallel.Another possibility isx + y = 1 and 2x + 2y = 2In this case there are an infinite number of solutions. Graphically, the two lines are coincidet, so that every point on the common line is a solution. There is, therefore, no unique solution.Yet another situation can arise when the domain of the equations is restricted.For example,x2 + y2 = -1 where x and y are real along with any other equation in x and y.


What is the meaning of a system of linear equation that are dependent?

It means that at least one of the equations can be expressed as a linear combination of some of the other equations. A linear combination of equations is the addition (or subtraction) of equations. And since an equation can be added several times, it includes multiples of equations. For example, if you have x + 2y = 3 and 2x + y = 4 Then adding 2 times the first and 3 times the second gives 8x + 7y = 18 This is, therefore, dependent on the other 2. If you have n unknown variables, there will be a unique solution if, and only if, you must have a set of n independent linear equations.