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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.
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What are two equations that have the same solution?
equal equations.
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?
It is not clear what the question requires. Yes, there are plenty of equations that have the same solution. For example, each and every equation of direct proportionality has the solution (0, 0). So what? every polynomial of the form y = anxn + an-1xn-1 + ... + a1x + a0 has the solution (0, a0). Again, so what?
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 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.
