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How do you know if a quadratic equation will have whether or not it will have solutions?
Factorise it!
How do you know when a equation has an infinte number of solutions?
-- A single equation with more than one variable in it has infinitely many solutions. -- An equation where the variable drops out has infinitely many solutions. Like for example x2 + 4x -3 = 0.5 (2x2 + 8x - 6) As mean and ugly as that thing appears at first, you only have to massage it around for a few seconds to get -3 = -3 and that's true no matter what 'x' is. So any value for 'x' is a solution to the equation, which means there are an infinite number of them.
2y - 12x equals -6?
2y-12x=-6 is the equation of a line. It has infinite number of solutions which are all the points one the line. We can rewrite the equation as 2y=12x-6 and then divide both sides by 2.This gives us y=6x-3. From this we know the equation describes a line with y intercept -2 and slope 6.
What is 2n plus 14?
This equation has no value, as the value of n could be anything, giving this equation an infinite number of answers. To answer this equation, you either need to know what n is, or have an equals sign.
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.
