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How can you tell when an equation in one variable has infinitely many solutions or no solutions?
There is no simple method. The answer depends partly on the variable's domain. For example, 2x = 3 has no solution is x must be an integer, or y^2 = -9 has no solution if y must be a real number but if it can be a complex number, it has 2 solutions.
How many total solutions are there to any quadratic equation?
2
Is it possible for an equation to have many solutions and can an equation have no solutions?
Yes and yes. eg x = y + 1 has an infinite number of solutions, and {sin(x) + cos(x) = 2} does not have a solution.
What are some solutions to the equation 25x2-100 equals 0?
How many are you expecting ? How will you know if we give you all of them,or only some of them ?Since the highest power of the variable in the equation is '2', ("x2"),the equation has exactly two solutions.25x2 - 100 = 0Divide each side by 25:x2 - 4 = 0Add 4 to each side:x2 = 4Take the square root of each side:x = +4 and -4And there are your two solutions.
How do you find several solutions of an equation in 2 variables?
-- Pick a number out of a hat or a telephone book, or ask the person standing next to you to give you a number. -- Assign that number to one of the variables. -- Solve the equation for the other variable. -- This gives you one "ordered pair" solution of the equation. -- Repeat, as many times as you want. You will never run out of solutions, and you will never find all of them, as there are an infinite number of them.
