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You know when an equation has a unique solution when there is only one variable in it. (APOLOGIES)
(RESPONSE: the question was categorized under "Linear Algebra". x^2 is non-linear and is thus not allowed, nor are sin x, x^3, log x, 2^x, etc etc. However, you are correct if you consider non-linear equations. Unfortunately, I am not sure there is a method to determine the number of solutions to non-linear equation.)
If there are more than one variable, each variable over the first will be free, and give you infinite solutions - with each additional variable adding another dimension to your solution.
(RESPONSE: See above response with regards to this topic being categorized under "Linear Algebra". My statement is true in Linear Algebra. Furthermore, Row Reduced Echelon Form and augmented matrices are the most fundamental concepts in Linear Algebra. Under normal circumstances, I would agree with you. However, this question was categorized under "Linear Algebra", so I presumed that the person asking the question is a college student.)
In general, you know that a system of equations has a unique solution when the row reduced echelon form of the augmented matrix has a pivot position in every column, except for the right most column which is the solution. If you do not have an augmented matrix, then the RREF will have a pivot position in every column.
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How do you know if a value a is a solution to an equation?
If this value a satisfy the equation, then a is a solution for that equation. ( or we can say that for the value a the equation is true)
How do you know if an equation is equivalent?
An equation is equivalent to another equation, if they have the same solution.
Which type of solution in equation 3x plus 4y equals 12 is this unique solution?
No. The equation describes a straight line and the coordinates of any one of the infinitely many points on the line is a solution.
How many solutions does x equals 8have?
A solution to an linear equation cx + d = f is in the form x = a for some a, we call a the solution (a might not be unique). Rewrite your sentence: x = 8, 8 is unique. So how many solution does it have?
What is the difference between a situation and a solution equation?
A situation equation follows the order of the story problem.For instance:Johnny has 8 apples, he eats some, and has 3 left.The situation equation would be: 8 - a = 3A solution equation is the equation that would help you find the solution. Your brain doesn't automatically know what "a" is, it has to rearrange the order of the equation and then solve.The solution equation would be: 8 - 3 = a, then you would solve it.
How do you know if a value a is a solution to an equation?
If this value a satisfy the equation, then a is a solution for that equation. ( or we can say that for the value a the equation is true)
How do you know if an equation is equivalent?
An equation is equivalent to another equation, if they have the same solution.
Which type of solution in equation 3x plus 4y equals 12 is this unique solution?
No. The equation describes a straight line and the coordinates of any one of the infinitely many points on the line is a solution.
Why are systems of equations important?
A single equation is several unknowns will rarely have a unique solution. A system of n equations in n unknown variables may have a unique solution.
How many solutions does x equals 8have?
A solution to an linear equation cx + d = f is in the form x = a for some a, we call a the solution (a might not be unique). Rewrite your sentence: x = 8, 8 is unique. So how many solution does it have?
Can anyone help solve this equation 5x y equals 10?
Nobody can help you find a solution until you get another equation to go along with this one. Your equation has two variables in it ... 'x' and 'y' ... so it has no unique solution all by itself.
What is the condition for unique solution of linear equation?
The equations are consistent and dependent with infinite solution if and only if a1 / a2 = b1 / b2 = c1 / c2.
Why do we represent the solution to an inequality with a graph on a number line but we don't do the same for the solution to an equation?
An equation has an equal sign, which means that we know what the variable is equal to :)
What is the solution to an equation?
a solution to an equation is the answer
What is the difference between a situation and a solution equation?
A situation equation follows the order of the story problem.For instance:Johnny has 8 apples, he eats some, and has 3 left.The situation equation would be: 8 - a = 3A solution equation is the equation that would help you find the solution. Your brain doesn't automatically know what "a" is, it has to rearrange the order of the equation and then solve.The solution equation would be: 8 - 3 = a, then you would solve it.
What is the difference in solution and equation?
A solution is the answer to an equation.
How do you know when a number is not a solution of an equation?
When you put the number in place of the variable (like maybe the 'x' or the 'y') wherever the variable occurs in the equation, and the statement you get out of all the numbers you have is not true, then you know the number is not a solution.
