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Does every pair of linear simultaneous equations have a solution?
Actually not. Two linear equations have either one solution, no solution, or many solutions, all depends on the slope of the equations and their intercepts. If the two lines have different slopes, then there will be only one solution. If they have the same slope and the same intercept, then these two lines are dependent and there will be many solutions (infinite solutions). When the lines have the same slope but they have different intercept, then there will be no point of intersection and hence, they do not have a solution.
What is the solution of a system of linear equations in two variables?
The solution of a system of linear equations is a pair of values that make both of the equations true.
What are equations with the same solution?
Equations with the same solution are called dependent equations, which are equations that represent the same line; therefore every point on the line of a dependent equation represents a solution. Since there is an infinite number of points on a line, there is an infinite number of simultaneous solutions. For example, 2x + y = 8 4x + 2y = 16 These equations are dependent. Since they represent the same line, all points that satisfy either of the equations are solutions of the system. A system of linear equations is consistent if there is only one solution for the system. A system of linear equations is inconsistent if it does not have any solutions.
What system of equations has no solution?
A system of equations will have no solutions if the line they represent are parallel. Remember that the solution of a system of equations is physically represented by the intersection point of the two lines. If the lines don't intersect (parallel) then there can be no solution.
Why a system of linear equations cannot have exactly two solutions?
A system of linear equations can only have: no solution, one solution, or infinitely many solutions.
What are equations with same solution called?
There is no special name. Two totally unrelated equations could have the same solution(s).
What is the consistent equation in mathematics?
Consistent equations are two or more equations that have the same solution.
How can you tell that an equation has the same solution as the original equation?
If the two equations are linear transformations of one another they have the same solution.
Does every pair of linear simultaneous equations have a solution?
Actually not. Two linear equations have either one solution, no solution, or many solutions, all depends on the slope of the equations and their intercepts. If the two lines have different slopes, then there will be only one solution. If they have the same slope and the same intercept, then these two lines are dependent and there will be many solutions (infinite solutions). When the lines have the same slope but they have different intercept, then there will be no point of intersection and hence, they do not have a solution.
Equations that have the same solution are called?
Equivalent equations
What do you call equations that have the same solution?
They are simultaneous equations
What are equivalant equations?
Equivalent equations are equations that have the same solution set.
How could you show that two equations aren't equivalent?
One way would be to solve the two equations. If they have exactly the same solution set, they are equivalent. Otherwise they are not.
A definition of a solution to a system of equations?
A system of equations is a set of two or more equations with the same variables, graphed in the same coordinate plane
Two or more equations with the same solution?
2x + 3 = 7 and x = 2 3y - 5 = 7 and y = 4
The graph of a system of equations with the same slope and the same y intercepts will have no solution?
The statement - The graph of a system of equations with the same slope and the same y intercepts will have no solution is True
What equations that same solution set over a given domain?
Equivalent Equations
