For which values of a the system has no solution?

For which values of a the system has no solution?

A system has no solutions if the lines are parallel. When solving the system, if you get a false statement (a number equal to a different number) this means there are no solutions.

How can you determine when an equation has no solution one solution or infinite solutions by using an equation?

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.

How do you know if a system of equations has one solution?

When both equations have the same slope, but not the same y-intercept, they’ll be parallel to each other and no intersections means no solutions. When both equations have different slopes than regardless of the y-intercept they’ll intersect for certain, therefore it has exactly one solution.

What is the best method for solving a system of equations?

Graphing: Graphing is the best method to use when introducing a new student to solving systems of two equations in two variables, because it gives them a visiual to recognize what they are looking for.

How do you solve 2 equations with 2 variables?

In a two-variable problem rewrite the equations so that when the equations are added, one of the variables is eliminated, and then solve for the remaining variable. Step 1: Multiply equation (1) by -5 and add it to equation (2) to form equation (3) with just one variable.

Can a linear system of two equations in three unknowns have a unique solution?

The three planes could be the same, so that a solution to one equation will be the solution to the other two equations. All three equations could be different but they intersect on a line, which has infinite solutions (see below for a graphical representation).

How many solutions can a system of 3 linear equations with 5 variables have?

(a) A homogeneous system of 3 equations in 5 unknowns. Since there are more unknowns than equations, there are infinitely many solutions.

How do you know if a system has no solution?

Consistent and Dependent Systems

1. If a consistent system has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line.
2. 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 condition for 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.

What is meant by 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 are infinitely many solutions?

Having infinitely many solutions means that you couldn’t possibly list all the solutions for an equation, because there are infinite. Sometimes that means that every single number is a solution, and sometimes it just means all the numbers that fit a certain pattern.

What is the difference between no solution and infinitely many solutions?

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.

Does the system have one none or infinite solutions?

Consistent systems are systems which have at least one solution. If the system has exactly one, unique solution then it is independent. If the system has infinite solutions, then it is called dependent.

What does 0 0 mean in a equation?

If you end with 0=0 , then it means that the left-hand side and the right-hand side of the equation are equal to each other regardless of the values of the variables involved; therefore, its solution set is all real numbers for each variable.

How do you tell if there are infinitely many solutions?

If a system has infinitely many solutions, then the lines overlap at every point. In other words, they’re the same exact line! This means that any point on the line is a solution to the system. Thus, the system of equations above has infinitely many solutions.