Sometimes we come across equations that don’t have any solutions, and even some that have an infinite number of solutions However, some equations have an infinite number of solutions or no solutions The case where an equation has no solution is illustrated in the next examples.
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So how do you tell if an equation has one solution, no solution, or infinite solutions
The trick is to look at the coefficients and constant terms of each given equation in the system of equations.
Still others have an infinite number How many solutions can you find for the problems below Solve for x, where possible. Solve linear equations in one variable
Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. When you solve an equation and come up with a false statement like this one, there is no solution Anytime you solve an equation and get the same result on each side of the equal sign, or a true statement, the problem has infinite solutions and all real numbers are the solution. If we can solve the equation and get something like x=b where b is a specific number, then we have one solution
If we end up with a statement that's always false, like 3=5, then there's no solution
If we end up with a statement that's always true, like 5=5, then there are infinite solutions. Learn how to tell if a system of equations has one, no, or infinite solutions This sat math guide explains patterns and strategies to solve these problems confidently. You're probably most familiar with equations that have one solution
