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If a system has an infinite number of solutions does it follow that any ordered pair is a solution?
No, this is not necessarily the case. A function can have an infinite range of solutions but not an infinite domain. This means that not every ordered pair would be a solution.
How do you know when an equation has infinitely many solutions?
When trying to solve an equation and you end up with the exact same number on both sides , like 10=10 then the equation has infinitely many solutions. If you end up with 2 different number on both side of the equation, like 3=5 then the equation has no solution. If there is a variable on one side and a number on the other, then there is one solution, e.g. x=4. In the equation 10=10 there is no variable such as x or y that we are trying to find the solution for. The equation x=x might be said to have an infinite number of solutions, because you can choose any value you like for x. More often you would say that "x is indeterminate". So if your equation always turns out to be satisfied for any x you choose, then there is an infinity of solutions and the equation does not represent anything useful. Or, for example, it may have a result such as "true for all even numbers", and you may not be aware in advance that this might happen. Or another example might be sin(x)=0 which has solutions for all values for those x which are integer multiples of 180 degrees. The only way is to solve the equation and see what appears.
How would you know that your equation has infinite solutions without actually solving it?
In some cases, a knowledge of the function in question helps. For example, when you have multiple equations, if you have more equations than variables you will usually have infinite solutions. Another example is that certain functions are known to be periodic, for instance the trigonometric functions - so an equation such as sin(x) = 1/2 may have infinite solution, due to the periodicity.
How many solutions are there if the equation is zero of the discriminant?
To a mathematician there are 2 coinciding solutions although most people would consider theseas one solution.
What is the slope of the equation -6?
I assume you mean y = -6. The slope of this would be zero since it is a horizontal line. For the equation x = -6, the slope would be infinite since this is a vertical line.
What is the asnwer for m-3n equals 8?
This would be like the equation of a line, with infinite solutions.
Lsquare plus msquare plus nsquare equals 1?
This equation describes all the points on the unit sphere. There is an infinite number of solutions. Some quick integer solutions would be (1,0,0) and (0,1,0) and (0,0,1) which are the one the axes.
If a system has an infinite number of solutions does it follow that any ordered pair is a solution?
No, this is not necessarily the case. A function can have an infinite range of solutions but not an infinite domain. This means that not every ordered pair would be a solution.
Which method would you use to solve this equation5x plus 3y equals 10?
There are an infinite number of solutions to a single equation in two variables. So, in order to save myself time, the first thing I would do is go out and look for another equation to put along with the first one.
How do you know if a systems of equations have infinitely many solutions?
If there are less distinct equations than there are variables then there will be an infinite number of solutions.For example, you may have 3 equations with 3 unknowns, but if one of those equations is a multiple of another there there are only 2 distinct equations:2x + 3y + 5z = 1x + y - 2z = 104x + 6y + 10z = 2Equation (3) here is twice equation (2) so there are effectively only 2 distinct equations for 3 unknowns and thus there will be an infinite number of solutions. If any two equations are parallel then there is no solution; if equation (3) above was 2x + 3y + 5z = 2, then there are no solutions - subtracting equation 1 from (the new) equation 3 would result in 0 = 1 which is nonsense.
How do you know when an equation has an inifinite number of solutions?
x + 2=y x=y-2 Let y=3 x=3-2 x=1 Let y be 4 x=4-2 x=2 Hence, the no. of times you will assume the value of y, the value of x would also be changed. There is no end to assumptions for y. It could be 1,2,3,0,-1,-2,5,6 etc. Hence a linear equation has infinite number of solutions.
How do you know when an equation has infinitely many solutions?
When trying to solve an equation and you end up with the exact same number on both sides , like 10=10 then the equation has infinitely many solutions. If you end up with 2 different number on both side of the equation, like 3=5 then the equation has no solution. If there is a variable on one side and a number on the other, then there is one solution, e.g. x=4. In the equation 10=10 there is no variable such as x or y that we are trying to find the solution for. The equation x=x might be said to have an infinite number of solutions, because you can choose any value you like for x. More often you would say that "x is indeterminate". So if your equation always turns out to be satisfied for any x you choose, then there is an infinity of solutions and the equation does not represent anything useful. Or, for example, it may have a result such as "true for all even numbers", and you may not be aware in advance that this might happen. Or another example might be sin(x)=0 which has solutions for all values for those x which are integer multiples of 180 degrees. The only way is to solve the equation and see what appears.
The graph of every linear equation in two variables is a?
Probably a plane since there would be an infinite number of lines to make a complete plane.
What would be the solutions for the equation 9 and -1?
10
What does the discriminant tell you?
The discriminant tells you how many solutions there are to an equation The discriminant is b2-4ac For example, two solutions for a equation would mean the discriminant is positive. If it had 1 solution would mean the discriminant is zero If it had no solutions would mean that the discriminant is negative
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.
How many planes can pass through one point?
I would say that there are an infinite number of planes that can pass through a pair of skew lines. In order to find the equation of a plane, all you need is three points. take two points off of one line and one point off of the other line and you should be able to derive the equation of a plane. Since the number of points on a line is infinite, an infinite number of planes can be derived.
