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What are the three kinds of linear equations?
The three types of linear equations are: Consistent Dependent, Consistent Independent, and Inconsistent.
What are the three types of systems of linear equations and their characteristics?
Independence:The equations of a linear system are independent if none of the equations can be derived algebraically from the others. When the equations are independent, each equation contains new information about the variables, and removing any of the equations increases the size of the solution set.Consistency:The equations of a linear system are consistent if they possess a common solution, and inconsistent otherwise. When the equations are inconsistent, it is possible to derive a contradiction from the equations, such as the statement that 0 = 1.Homogeneous:If the linear equations in a given system have a value of zero for all of their constant terms, the system is homogeneous.If one or more of the system's constant terms aren't zero, then the system is nonhomogeneous.
What the system of linear equation in two variabes which has no solution?
For two linear equations, they are equations representing parallel lines. (The lines must not be concurrent because if they are, you will have an infinite number of solutions.) For example y = mx + b and y = mx + c where b and c are different numbers are two non-concurrent parallel lines. The equations have no solution. With more than two linear equations there is much more scope. Unless ALL the lines meet at one point, the system will not have a solution. So a system consisting of equations defining the three lines of a triangle, for example, will not have a solution.
How many of the different kinds of solution sets are possible in two linear equations?
Three different kinds: none, one and infinitely many.
How many solutions does a system of linear equations in three variables have?
1
What are the three kinds of linear equations?
The three types of linear equations are: Consistent Dependent, Consistent Independent, and Inconsistent.
Do equations with different slopes and different y-intercepts have a solution?
TWO linear equations with different slopes intersect in one point, regardlessof their y-intercepts. That point is the solution of the pair.However, this does not mean that three (or more) equations in two variables, even if they meet the above conditions, have a solution.
What are the three types of systems of linear equations and their characteristics?
Independence:The equations of a linear system are independent if none of the equations can be derived algebraically from the others. When the equations are independent, each equation contains new information about the variables, and removing any of the equations increases the size of the solution set.Consistency:The equations of a linear system are consistent if they possess a common solution, and inconsistent otherwise. When the equations are inconsistent, it is possible to derive a contradiction from the equations, such as the statement that 0 = 1.Homogeneous:If the linear equations in a given system have a value of zero for all of their constant terms, the system is homogeneous.If one or more of the system's constant terms aren't zero, then the system is nonhomogeneous.
What the system of linear equation in two variabes which has no solution?
For two linear equations, they are equations representing parallel lines. (The lines must not be concurrent because if they are, you will have an infinite number of solutions.) For example y = mx + b and y = mx + c where b and c are different numbers are two non-concurrent parallel lines. The equations have no solution. With more than two linear equations there is much more scope. Unless ALL the lines meet at one point, the system will not have a solution. So a system consisting of equations defining the three lines of a triangle, for example, will not have a solution.
How many of the different kinds of solution sets are possible in two linear equations?
Three different kinds: none, one and infinitely many.
How many solutions does a system of linear equations in three variables have?
1
Kinds of system of linear equation in two variables?
There are three kinds:the equations have a unique solutionthe equations have no solutionthe equations have infinitely many solutions.
Does the solution to a system of three equations in three variables is always one point?
No. There could be no solution - no values for x, y, and z so that the 3 equations are true.
What are the three types of outcomes for linear equations?
All the lines meet at one point: a single solution. All the lines are the same: infinitely many solutions. At least one of the lines does not pass through the point of intersection of the others: no solution.
How do you write linear equations?
Linear equations take the form y= mx+b wherem is the slope [rise(y)/run(x) on a graph]x is the x-value any point on the graphy is the y-value of any point on the graphb is the y-intercept on the graphLinear equations take the form a1x1 + a2x2 + a3x3 + ... + anxn + an+1 = 0Each ai represents a constant, xi a variable.The equation above is linear in n dimensions. In two dimensions, linear equations are typically written ax + by = c. In three dimensions, ax + by + cz = d. After that, the form given above (with the subscripts) is preferred.Any system of n equations and n unknowns may have a unique solution. If two of the equations are multiples of each other, the solution set will not be unique, but represent a line, plane, or subspace. It is also possible the system may have no solution, such as the following:5x + 10y = 55x + 10y = 20This system represents two parallel lines--there is no solution.
What has only one solution?
There are many possible answers to this question. Some of these areA linear equation.A system of n independent linear simultaneous equations is n unknowns.Quadratic equations in which the two real roots are coincident.Cubic equation where either all three roots are coincident or, if the domain is real, then when two of the roots are imaginary.
What is the disadvantage of using the substitution method in solving linear equations rather than the graph method?
There are no disadvantages. There are three main ways to solve linear equations which are: substitution, graphing, and elimination. The method that is most appropriate can be found by looking at the equation.
