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How many solutions exist for the following system of equations?
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How many types of solutions of a system of two linear equations in two unknowns can exist?
There is only one type of solution if there are two linear equations. and that is the point of intersection listed in (x,y) form.
Do there exists solution of all types of differential equations?
No, analytical solutions do not always exist. That is to say, the answer need not be a function. However, it is possible to find numerical solutions.
What math equation did sonya kovalskaya figure out?
She did not figure out a particular equation but found the set of conditions under which solutions to a class of partial differential equations would exist. This is now known as the Cauchy-Kovalevskaya Theorem.
How many solutions exist for the system of equation x plus 6y equals 12 plus 2x plus 12y equals 1?
zero solutions. If you plot these two lines, you will see that they are parallel and do not intersect.
How many different kinds of solutions do two linear equations have?
Let the number of unknowns be N. The solution space may have N, N-1, ..., 0 dimensions or may not exist. If a solution exists and the dimension of the solution space is 0, then there is exactly one solution,. If the dimension of the solution space > 0, then there are infinitely many solutions.
How many types of solutions of a system of two linear equations in two unknowns can exist?
There is only one type of solution if there are two linear equations. and that is the point of intersection listed in (x,y) form.
Do there exists solution of all types of differential equations?
No, analytical solutions do not always exist. That is to say, the answer need not be a function. However, it is possible to find numerical solutions.
When will a homogeneous system of equations be inconsistent?
A homogeneous system of eqs: Ax=0 will always be consistent, since x=0 is always a possible solution. However, if det(A)=0 then there will be infinite solutions, as |A|=0 implies that either no solutions or infinitely many exist, and it is impossible for no solutions to exist to Ax=0. If det(A) is non 0, then x=0 is the only solution, as |A| is not equal to 0 implies a unique solution only!(in this case x=0). Hope this helps!
Can a system of linear equation have more than one solutions?
No. A linear equation represents a straight line and the solution to a set of linear equations is where the lines intersect; two straight lines can only intersect at most at a single point - two straight lines may be parallel in which case they will not intersect and there will be no solution. With more than two linear equations, it may be that they do not all intersect at the same point, in which case there is no solution that satisfies all the equations together, but different solutions may exist for different subsets of the lines.
Does any homogeneous system have nontrivial solution?
x+y=0 2x+2y=0 This homogeneous system has infinitely many non-trivial solutions. If you are looking for exactly one non-trivial solution, no such system exists. the system may or may not have non trivial solution. if number of variables equal to number of equations and given matrix is non singular then non trivial solution does not exist
Are solutions always have a liquid?
No, solid solutions also exist.
What math equation did sonya kovalskaya figure out?
She did not figure out a particular equation but found the set of conditions under which solutions to a class of partial differential equations would exist. This is now known as the Cauchy-Kovalevskaya Theorem.
Why ferric ions do not exist in solution?
Ferric ions exist in solutions.
Are all solutions must be in the liquid state?
False: solid solutions exist.
How many solutions exist for the system of equation x plus 6y equals 12 plus 2x plus 12y equals 1?
zero solutions. If you plot these two lines, you will see that they are parallel and do not intersect.
What are some equations that are not balancing?
all equations balance as the theory of conservation of mass states that no mass should be lost, so all equations should balance
How many different kinds of solutions do two linear equations have?
Let the number of unknowns be N. The solution space may have N, N-1, ..., 0 dimensions or may not exist. If a solution exists and the dimension of the solution space is 0, then there is exactly one solution,. If the dimension of the solution space > 0, then there are infinitely many solutions.
