Can a linear equation have two solutions?
Most linear systems you will encounter will have exactly one solution. However, it is possible that there are no solutions, or infinitely many. (It is not possible that there are exactly two solutions.) The word unique in this context means there is a solution, and it’s the only one.
Which equation has only 1 solution?
quadratic equation
A quadratic equation has exactly one real number solution.
What is a one solution equation?
If solving an equation yields a statement that is true for a single value for the variable, like x = 3, then the equation has one solution. If solving an equation yields a statement that is always true, like 3 = 3, then the equation has infinitely many solutions.
Can a linear equation have 3 solutions?
No, a system of linear equations has either a unique solution, no solutions, or infinitely many solutions. If there are two or more solutions, then any linear combination of them is another solution. In 3-D, a linear equation determines a plane.
What does it mean when there is only one solution?
So far we have looked at equations where there is exactly one solution. No solution would mean that there is no answer to the equation. It is impossible for the equation to be true no matter what value we assign to the variable. Infinite solutions would mean that any value for the variable would make the equation true.
How do you know if a linear equation has no solution?
Correct answer: 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.
What is a linear equation with no solution?
No solution would mean that there is no answer to the equation. It is impossible for the equation to be true no matter what value we assign to the variable. Infinite solutions would mean that any value for the variable would make the equation true. No Solution Equations.
How do you tell if a linear equation has no solution?
How many solutions does a linear equation in one variable have?
Every linear equation in one variable has a one and unique solution. If the equation has two or more variables then it becomes a linear equation in two variables or linear equations in three variables and so on and the number of solutions varies as per the count of variables an equation contains.
How do you know if an equation has only one solution?
Hence, the given linear equation has only one solution i.e. x = 80. From the above examples, we see that the variable x does not disappear after solving & we say that the linear equation will have one solution if it is satisfied by exactly one value of the variable. Example 1: Consider the equation 7x – 35 = 5x + 2x – 27.
When does a linear equation have zero or no solution?
From the above examples, we can see that the variable x disappears / gets eliminated & hence we say that the linear equation will have Zero or no solution if it can’t be satisfied by any value of the variable or there does not exist any value of the variable which makes the given equation a true statement.
How do you find the unique solution of a linear equation?
The linear equation in one variable always has a unique solution. The unique solution of a linear equation represents that there exists only one point, which on substitution, L.H.S becomes equal to R.H.S. In the case of simultaneous linear equations in two variables, the solution should be an ordered pair (x, y).