How do you tell if an equation is consistent dependent or independent?
If a system has at least one solution, it is said to be consistent . 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.
How many solutions does this system of equations have Y =- 2x 2 2y 4x 4?
The two lines have the same equation, hence there are infinite solutions (since the two lines lie one on top of one another).
How do you determine whether a system has one solution no solution or infinitely many solutions?
A linear system has one solution when the two lines comprising the system intersect once. A linear system has many (infinite) solutions when the two lines are the same (such as y=x+3 and 2y=2x+6 ).
How do you determine if a system of equations has a unique solution?
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 find the independent equation?
In order for the system to be independent, the equations must have different lines when they are graphed. If the equations have different slopes and/or intercepts, they will create different lines. For our next example, we will identify the slope and intercept of each equation in a system of equations.
What is a consistent dependent equation?
Consistent Dependent: A system of linear equations is consistent dependent if it has an infinite number of solutions. When this is the case, the graphs of the lines in the system are the same, meaning the equations in the system represent the same line.
How many solutions does Y 2x 2 have?
These are three possible solutions to the equation.
What is the solution to the system of equations?
A solution to a system of equations is a set of values for the variable that satisfy all the equations simultaneously. In order to solve a system of equations, one must find all the sets of values of the variables that constitutes solutions of the system.
How do you find an equation that has no solution?
Correct answer: The coefficients are the numbers alongside the variables. The constants are the numbers alone with no variables. If the coefficients are the same on both sides then the sides will not equal, therefore no solutions will occur.
What is unique solution formula?
The formula of unique solution is for a given pair of linear equations is: a1x + b1y + c1 = 0. a2x + b2y + c2 = 0. The solution is said to be unique solution when, This is the formula of unique solution.
What is the 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.