Tereasa Brasher asked, updated on February 5th, 2021; Topic:
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If we end up with the same term on both sides of the equal sign, such as 4 = 4 or 4x = 4x, then we have infinite solutions. If we end up with different numbers on either side of the equal sign, as in 4 = 5, then we have no solutions.
Although, how do you tell if an equation has one infinite or no solutions?
So, how do you find out how many solutions an equation has? The total number of solutions should equal the highest exponent in the binomial: one solution for x, two solutions for x^2, or three solutions for x^3. Some binomials have repeat solutions. For example, the equation x^4 + 2x^3 = x^3(x + 2) has four solutions, but three are x = 0.
Anywho, which systems of equations have infinite solutions?
If a system has infinitely many solutions, then the lines overlap at every point. In other words, they're the same exact line! This means that any point on the line is a solution to the system. Thus, the system of equations above has infinitely many solutions.
Is 0 0 infinite or no solution?
For an answer to have an infinite solution, the two equations when you solve will equal 0=0 . ... If you solve this your answer would be 0=0 this means the problem has an infinite number of solutions. For an answer to have no solution both answers would not equal each other.
When a problem has no solution you'll end up with a statement that's false. For example: 0=1 This is false because we know zero can't equal one. Therefore we can conclude that the problem has no solution. You can solve this as you would any other equation.
Solving Equations in One Variable A solution to an equation is a number that can be plugged in for the variable to make a true number statement. 3(2)+5=11 , which says 6+5=11 ; that's true! So 2 is a solution.
In this case, each point on the line is a solution. If there are infinitely many solutions of the given pair of linear equations, the equations are called dependent (consistent). If the lines are parallel, there is no solution for the pair of linear equations.
Infinite Solutions If the graphs of the equations do not intersect (for example, if they are parallel), then there are no solutions that are true for both equations. If the graphs of the equations are the same, then there are an infinite number of solutions that are true for both equations.
In short, the multiplicative identity is the number 1, because for any other number x, 1*x = x. So, the reason that any number to the zero power is one is because any number to the zero power is just the product of no numbers at all, which is the multiplicative identity, 1.
0/0 is undefined. If substituting a value into an expression gives 0/0, there is a chance that the expression has an actual finite value, but it is undefined by this method. We use limits (calculus) to determine this finite value.
Three Types of Solutions of a System of Linear Equations There are three possible outcomes for a system of linear equations: one unique solution, infinitely many solutions, and no solution. This video shows an example of each type of outcome.
A system has infinitely many solutions when it is consistent and the number of variables is more than the number of nonzero rows in the rref of the matrix. For example if the rref is has solution set (4-3z, 5+2z, z) where z can be any real number.
It is called the Discriminant, because it can "discriminate" between the possible types of answer: when b2 − 4ac is positive, we get two Real solutions. when it is zero we get just ONE real solution (both answers are the same) when it is negative we get a pair of Complex solutions.
If you get a positive number, the quadratic will have two unique solutions. If you get 0, the quadratic will have exactly one solution, a double root. If you get a negative number, the quadratic will have no real solutions, just two imaginary ones.
The solution x = 0 means that the value 0 satisfies the equation, so there is a solution. “No solution” means that there is no value, not even 0, which would satisfy the equation. Also, be careful not to make the mistake of thinking that the equation 4 = 5 means that 4 and 5 are values for x that are solutions.