In a set of linear simultaneous equations, a unique solution exists if and only if, (a)
the number of unknowns and the number of equations are equal
, (b) all equations are consistent, and (c) there is no linear dependence between any two or more equations, that is, all equations are independent.
How do you determine if a system has a unique solution?
Condition for Unique Solution to Linear Equations
A system of linear equations
ax + by + c = 0 and dx + ey + g = 0
will have a unique solution if the two lines represented by the equations ax + by + c = 0 and dx + ey + g = 0 intersect at a point. i.e., if the two lines are neither parallel nor coincident.
Does the system have a unique solution?
The three types of solution sets: A system of linear equations
can have no solution
, a unique solution or infinitely many solutions. A system has no solution if the equations are inconsistent, they are contradictory. for example 2x+3y=10, 2x+3y=12 has no solution. is the rref form of the matrix for this system.
What is a unique solution?
By the term unique solution, one
mean to say that only one specific solution set exists for a given equation
. … So, if we have two equations, then unique solution will mean that there is one and only point at which the two equations intersect.
What is the condition for unique solution?
to have unique solution (consistent solution), the condition which must be satisfied is
that the ratio of the coefficients of x should not be equal to the ratio of the coefficients of y in the pair of linear equations.
What does a unique solution look like?
In a set of linear simultaneous equations, a unique solution exists if and only if, (a) the number of unknowns and the number of equations are equal, (b) all
equations
are consistent, and (c) there is no linear dependence between any two or more equations, that is, all equations are independent.
How do you know if two equations have no solution?
Explanation: When finding how many solutions an equation has you need to look at the
constants and coefficients
. The coefficients are the numbers alongside the variables. … If the coefficients are the same on both sides then the sides will not equal, therefore no solutions will occur.
What is the formula of no solution?
If (a
1
/a
2
) = (b
1
/b
2
) ≠ (c
1
/c
2
)
, then there will be no solution. This type of system of equations is called an inconsistent pair of linear equations.
What determinant has no solution?
If the
determinant of a matrix is zero
, then the linear system of equations it represents has no solution. In other words, the system of equations contains at least two equations that are not linearly independent.
Can an underdetermined system have a unique solution?
Theorem. If there are fewer equations than variables, then the system is called underdetermined and
cannot have a unique solution
. In this case, there are either infinitely many or no solutions. … A system with more equations than variables is called overdetermined.
What is a system with no solution?
A system of two linear equations can have one solution, an infinite number of solutions, or no solution. … If a system has no solution, it is said to be
inconsistent
. The graphs of the lines do not intersect, so the graphs are parallel and there is no solution.
What is the meaning of no solution?
No solution would mean
that there is no answer to the equation
. It is impossible for the equation to be true no matter what value we assign to the variable. Infinite solutions would mean that any value for the variable would make the equation true. … Note that we have variables on both sides of the equation.
What is the formula of infinitely many solutions?
An infinite solution
has both sides equal
. For example, 6x + 2y – 8 = 12x +4y – 16. If you simplify the equation using an infinite solutions formula or method, you’ll get both sides equal, hence, it is an infinite solution. Infinite represents limitless or unboundedness.
What are the 3 types of solutions in math?
The three types of solution sets: A system of linear equations can have no solution,
a unique solution or infinitely many solutions
. A system has no solution if the equations are inconsistent, they are contradictory.
What does an infinite solution look like?
When a problem has infinite solutions, you’ll end up with a statement that’s
true no matter what
. For example: 3=3 This is true because we know 3 equals 3, and there’s no variable in sight. Therefore we can conclude that the problem has infinite solutions. You can solve this as you would any other equation.
When two lines are parallel the system has infinite number of solutions?
When the lines are parallel, there are
no solutions
, and sometimes the two equations will graph as the same line, in which case we have an infinite number of solutions.
