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If a system of linear equations has many solutions what would be the correct mathematical description of the system?
dependent
Solve this system of equations using the addition method x plus y equals 6?
When talking about a "system of equations", you would normally expect to have two or more equations. It is quite common to have as many equations as you have variables, so in this case you should have two equations.
When you solve a system of equations algebraically how can you tell whether the system has zero one or an infinite number of solutions?
Compare the equations. If it has the same slope it most likely will be parallel which means it has 0 solutions. However, if you plug in points and they match up exactly it would have an infinite amount of solutions. The only way it would intersect more than once or 2 then would be if it was a parabola which would have a x^2 value typically. If it has 1 solution it means it would intersect once.
Why are linear equations called linear equations?
Because, if plotted on a Cartesian plane, all solutions to the equation would lie on a straight line.
What would be a solution to a system?
The solution would be the point of intersection of the graphical representation of all equations within the system.
If a system of linear equations has many solutions what would be the correct mathematical description of the system?
dependent
Does the graph of a system of equations with different slopes have no solutions?
The graph of a system of equations with the same slope will have no solution, unless they have the same y intercept, which would give them infinitely many solutions. Different slopes means that there is one solution.
Solve this system of equations using the addition method x plus y equals 6?
When talking about a "system of equations", you would normally expect to have two or more equations. It is quite common to have as many equations as you have variables, so in this case you should have two equations.
Systems of equations with different slopes and different y-intercepts have no solutions?
No the only time that a system of equations would have no solutions is when the two equations have the same slope but different y-intercepts which would mean that they are parallel lines. However, if they have different slopes and different y-intercepts than the solution would be where the two lines intersect.
Imagine that you are given two linear equations in slope-intercept form. You notice that the slopes are different but the y-intercepts are the same. How many solutions would you expect for this system?
infinintly many. for apex.
When you solve a system of equations algebraically how can you tell whether the system has zero one or an infinite number of solutions?
Compare the equations. If it has the same slope it most likely will be parallel which means it has 0 solutions. However, if you plug in points and they match up exactly it would have an infinite amount of solutions. The only way it would intersect more than once or 2 then would be if it was a parabola which would have a x^2 value typically. If it has 1 solution it means it would intersect once.
What is of system of equations?
It is essentially a list of equations that have common unknown variables in all of them. For example, a+b-c=3 4a+b+c=1 a-2b-7c=-2 would be a system of equations. If there are the same number of equations and variables you can usually, but not always, find the solutions. Since there are 3 equations and 3 variables (a, b, and c) in this example one can usually find the value of those three variables.
How would you know if a linear system has a solution?
One way is to look at the graphs of these equations. If they intersect, the point of intersection (x, y) is the only solution of the system. In this case we say that the system is consistent. If their graphs do not intersect, then the system has no solution. In this case we say that the system is inconsistent. If the graph of the equations is the same line, the system has infinitely simultaneous solutions. We can use several methods in order to solve the system algebraically. In the case where the equations of the system are dependent (the coefficients of the same variable are multiple of each other), the system has infinite number of solutions solution. For example, 2x + 3y = 6 4y + 6y = 12 These equations are dependent. Since they represent the same line, all points that satisfy either of the equations are solutions of the system. Try to solve this system of equations, 2x + 3y = 6 4x + 6y = 7 If you use addition or subtraction method, and you obtain a peculiar result such that 0 = 5, actually you have shown that the system has no solution (there is no point that satisfying both equations). When you use the substitution method and you obtain a result such that 5 = 5, this result indicates no solution for the system.
Why are linear equations called linear equations?
Because, if plotted on a Cartesian plane, all solutions to the equation would lie on a straight line.
What is an ordered pair that makes all equations in a system true?
That would be the "solution" to the set of equations.
Do four iterations to solve the following system of equations by Jacobi's method of iteration?
The question refers to the "following". In such circumstances would it be too much to expect that you make sure that there is something that is following?
What happens when every day speeds are put into the relativistic equations?
The solutions will be extremely similar to what you would get for equations in Newtonian physics. At everyday speeds the deviation from Newtonian mechanics is negligible.
