Yes and they will be of equal value
That has an infinite number of solutions. Choose any value for "a"; then divide 120 by that number to get "b".
In order for a system to have infinitely many solutions, it must contain an equation that could be solved by any set of variables. In simple terms, a two-variable system can only be solved through two distinct equations; however, if one of these equations becomes meaningless, or could be solved by any set of variables, the other equation becomes meaningless as well because any value of y could match a given value of x. In terms of linear algebra, or any set or matrices meant to represent a system, infinitely many solutions occur due to an all 0 row. After the system is reduced to row echelon form, an all 0 row indicates that all coefficients in a given equation are equal to 0, so it does not matter what the variables are. This means that the number of equations no longer equals the number of variables and it becomes impossible to solve through cancellation and back-substitution.
-- 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.
There are infinitely many ordered pairs that satisfy this equation. Supply any value for x, then solve for y to get the other part of the pair.
Strictly speaking the above equation is a tautological equation or an IDENTITY. An identity is true for all values of any variables that appear in it. Thus, the above "equation" is true for all value of x. - that is, it has infinitely many solutions.
Yes and they will be of equal value
There are infinitely many. For each value of x there is a value of y, and there are an infinite number of values of x to start with.
They Are infinitely many solutions for an equation when after solving the equation for a variable(let us suppose x),we get the expression 0 = 0. Or Simply L.H.S = R.H.S For Ex. x+3=3+x x can have any value positive or negative, rational or irrational, it doesn't matter the sequence will be infinite. And No Solutions when after solving the equations the expression obtained is unequal For Ex. x+3=x+5 for every value of x, The Value in L.H.S And R.H.S. will differ. Hence It Has No Solutions.
I suspect the answer depends on the value of t.
It is not appropriate to talk about "the" three solutions for this equations; the equation describes a straight line, and has an infinite number of solutions. Solve the equation for "y", substitute any value for "x", and calculate the corresponding value for "y", to get one opf these solutions.
That has an infinite number of solutions. Choose any value for "a"; then divide 120 by that number to get "b".
The equations are identical in value, ie the second is merely twice the first...
This has infinitely many solutions. The idea is to solve the equation for one of the variables, say for "y". The solution will be in terms of "x" in this case. Then, if you assign any value to "x", you can calculate the corresponding value for "y".
In order for a system to have infinitely many solutions, it must contain an equation that could be solved by any set of variables. In simple terms, a two-variable system can only be solved through two distinct equations; however, if one of these equations becomes meaningless, or could be solved by any set of variables, the other equation becomes meaningless as well because any value of y could match a given value of x. In terms of linear algebra, or any set or matrices meant to represent a system, infinitely many solutions occur due to an all 0 row. After the system is reduced to row echelon form, an all 0 row indicates that all coefficients in a given equation are equal to 0, so it does not matter what the variables are. This means that the number of equations no longer equals the number of variables and it becomes impossible to solve through cancellation and back-substitution.
-- 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.
There are infinitely many ordered pairs that satisfy this equation. Supply any value for x, then solve for y to get the other part of the pair.