How do you determine if a system is consistent inconsistent or dependent?
How do you determine if a system is consistent inconsistent or dependent?
If a consistent system has exactly one solution, it is independent .
- If a consistent system has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line.
- If a system has no solution, it is said to be inconsistent .
Is the following pair of linear equation consistent or inconsistent 6x 3y 10 0 2x y 9 0?
∴ The lines represented by the given equations are parallel.
How do you classify the system as consistent dependent consistent independent or inconsistent?
An ordered pair that satisfies all of the equations in a system is a solution to the system. Linear systems of equations can have one solution, no solution, or infinitely many solutions. Consistent Dependent: A system of linear equations is consistent dependent if it has an infinite number of solutions.
How can you tell if an equation is inconsistent?
Inconsistent System Let both the lines to be parallel to each other, then there exists no solution, because the lines never intersect. and the pair of linear equations in two variables is said to be inconsistent.
How do you find the consistency of a system of equations?
HOW TO CHECK CONSISTENCY OF LINEAR EQUATIONS USING MATRICES
- Step 1 : Find the augmented matrix [A, B] of the system of equations.
- Step 2 : Find the rank of A and rank of [A, B] by applying only elementary row operations. Note : Column operations should not be applied.
- Step 3 :
Which of the following pairs of linear equations are consistent inconsistent 3x 2y 5 2x 3y 7?
3x + 2y = 5, 2x – 3y = 7. Hint: For checking whether the pair of linear equations are consistent or inconsistent, we try to obtain values of x and y. If both x and y have a unique value then the system is consistent. The system becomes inconsistent when there exist no values of x and y that satisfy both the equations.
Which of the following pairs of linear equations are consistent or inconsistent 2x 3y 8 4x 6y 9?
On comparing the ratio, (a1/a2) , (b1/b2) , (c1/c2) find out whether 2x – 3y = 8 ; 4x – 6y = 9 are consistent or inconsistent. So, the equations are parallel to each other and they have no possible solution. Hence, the equations are inconsistent.
What makes a system inconsistent?
Which system of equation is inconsistent?
A system of equations is called an inconsistent system of equations if there is no solution because the lines are parallel. A dependent system of equations is when the same line is written in two different forms so that there are infinite solutions.
How many solutions does a consistent dependent system have?
infinite solutions
A dependent system of equations has infinite solutions, and an independent system has a single solution.
What is a Dependant system?
A dependent system of equations is when the same line is written in two different forms so that there are infinite solutions. These two situations occur when trying to solve for a system of equations. system of equations solution parallel dependent inconsistent.
Which of the following pairs of linear equations are consistent inconsistent XY 8 3x 3y 16?
(ii) x – y = 8, 3x – 3y =16 are parallel and have no solution. Hence, the pair of equations are inconsistent.
What is the number of solutions the pair of linear equations 4x 6y 9 and 2x 3y 6?
These equations have no solution.
What makes a system dependent?
In a system of linear equations, the equations are all linear, meaning that they form a straight line when graphed. The graphs of the equations may be parallel, intersect at one point, or form the same line. If the equations form the same line, we refer to it as a dependent system of linear equations.
What is dependent system?
A dependent system of equations is when the same line is written in two different forms so that there are infinite solutions. These two situations occur when trying to solve for a system of equations.
How do you prove a system of equations is inconsistent?
Inconsistent. If a system of equations has no solutions, then it is inconsistent. If the last column (in an augmented matrix) is a pivot column, that is, it has a pivot, then it’s inconsistent.
How do you find the consistency of an equation?
Consistent System
- i) If both the lines intersect at a point, then there exists a unique solution to the pair of linear equations. In such a case, the pair of linear equations is said to be consistent.
- ii) Consider two lines having equation to be-
- i) Consider the equation of the lines to be-
- Solution: