Question: What Makes A System Have No Solution?

How do you know if there is no solution or infinite solutions?

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..

Why is 1 0 1?

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.

When a system has no solution?

If a consistent system has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line. If a system has no solution, it is said to be inconsistent . The graphs of the lines do not intersect, so the graphs are parallel and there is no solution.

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 . Here is a problem that has an infinite number of solutions. If you solve this your answer would be 0=0 this means the problem has an infinite number of solutions.

What do you call a problem with no solution?

A set of equations with no solutions is called inconsistent if there is no simultaneous solution for the set.

Does 0 0 mean all real numbers?

2 Answers. If you end with 0=0 , then it means that the left-hand side and the right-hand side of the equation are equal to each other regardless of the values of the variables involved; therefore, its solution set is all real numbers for each variable.

Which equation has no solution 4x 2 =- 6?

Answer: Option A) |4x – 2| = – 6 has no solution. Since left hand side of function is in modulus, so it will always gives positive values but right hand side is – 6 , So, there are no values of x that make the equation true.

How do you tell if a system of inequalities has no solution?

Systems Without Solutions A graph of this system is shown below. The bounded regions of the two inequalities do not overlap, so there is no solution set. However, the existence of parallel lines does not necessarily indicate that there is no solution, it just means that there is the possibility of no solutions.

What the difference between no solution and all real numbers?

If the inequality states something untrue there is no solution. If an inequality would be true for all possible values, the answer is all real numbers.

What makes a no solution?

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. … This is because there is truly no solution—there are no values for x that will make the equation 12 + 2x – 8 = 7x + 5 – 5x true.

How do you tell if a function has no solution?

The coefficients are the numbers alongside the variables. The constants are the numbers alone with no variables. If the coefficients are the same on both sides then the sides will not equal, therefore no solutions will occur.

Which system of equation has no solution?

Since parallel lines never cross, then there can be no intersection; that is, for a system of equations that graphs as parallel lines, there can be no solution. This is called an “inconsistent” system of equations, and it has no solution. The third graph above, “Case 3”, appears to show only one line.

How do you know if an equation has two Solution?

A line can only cross another line in at most one place, so there can be at most one solution (x=3). A parabola, though, curves, so it can cross the x axis in two places. So if you have an equation like x^2 + 5x + 6 = 0, it can have two solutions.

What happens when an equation is 0 0?

If the elimination produces the equation 0=0, then the two equations are for the same line. This means that there are an infinite number of solutions.

What is an example of a no solution?

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. … So, we say this problem has no solution. This means no matter what number you put in for the variable x, you will never get anything that equals one another.

What is an example of one solution?

Linear Equations With one Solution On solving we have 7x = 35 or x = 5. The above linear equation is only true if x = 5 and hence the given linear equation has only one solution i.e. x = 5. Example 2: Consider the equation 9(x – 1) – 35 = 8x + 37. On solving we have 9x – 9 – 35 = 8x + 37.

What is the value of 0 by 0?

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.

How can you tell if an equation has infinitely many solutions?

An equation can have infinitely many solutions when it should satisfy some conditions. The system of an equation has infinitely many solutions when the lines are coincident, and they have the same y-intercept. If the two lines have the same y-intercept and the slope, they are actually in the same exact line.