Sage-Tips

How do you know if a pair of linear equations is consistent or inconsistent?

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.

Is it possible to have no answer to a system of two linear equations?

If the two lines intersect at one place, then the point of intersection is the solution to the system. If the two lines are parallel, then they never intersect, so there is no solution.

Can an equation be inconsistent and dependent?

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 could we have if we solve a system of linear equations in two variables?

There can be more than one solution to a system of equations. A system of linear equations will have one point of intersection, or one solution. To graph a system of equations that are written in standard form, you must rewrite the equations in slope -intercept form.

Is 3x 2y 5 consistent or inconsistent?

Therefore, these equations are consistent.

Which of the following pairs of linear equations are inconsistent *?

If a 1/ a 2 = b 1/ b 2 ≠ c 1 / c 2 , then a pair of linear equations has no solution. A pair of linear equations which has no solution is said to be an inconsistent pair of linear equations. Therefore, these linear equations are coincident pair of lines and thus have infinite number of possible solutions.

How do you know if there are infinitely many solutions?

Well, there is a simple way to know if your solution is an infinite solution. 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.

Can a linear system have two solutions?

Most linear systems you will encounter will have exactly one solution. However, it is possible that there are no solutions, or infinitely many. (It is not possible that there are exactly two solutions.) The word unique in this context means there is a solution, and it’s the only one.

Which of the following is an example of an inconsistent equation or contradiction?

Inconsistent equations is defined as two or more equations that are impossible to solve based on using one set of values for the variables. An example of a set of inconsistent equations is x+2=4 and x+2=6.

Can a system of linear equations have exactly two solutions explain why or why not by describing the 3 types of linear systems?

No. A system of linear equations in two variables may have zero, one, or infinitely many solutions.

Which of the following pairs of linear equations are inconsistent?

How do you prove a pair of equations are inconsistent?

Algebraically, when = = , then the lines coincides and the pair of equations is dependent and consistent. Let both the lines to be parallel to each other, then there exists no solution, because the lines never intersect. Algebraically, for such a case, = ≠ and the pair of linear equations in two variables is said to be inconsistent.

What is a consistent pair of linear equations?

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. In the graph given above, lines intersect at point which represents the unique solution of the system of linear equations in two variables.

What is the difference between consistent and inconsistent lines?

Answer: Consistent=lines intersect at point which represents the unique solution of the system of linear equations in two variables. Algebraically, if then, the linear equations’ pair is consistent. Inconsistent=lines which are parralel are inconsistent

What are the solutions of linear equations in one variable?

Solution of Linear Equations in One Variable 1 Clear the fraction x – 5 = 3 (x – 1) 2 Simplify Both sides equations 2x – 5 = 3x – 3 x = 3x + 2 x – 3x = 2 3 Isolate x