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What does one solution mean in math?
An equation may have zero, one, or more solutions (this is also true for a system of equations). The equation 2 + x = 5 has only solution, for example. x can only equal 3, so there is one solution. (An example of an equation with more that one solution is x2 = 4. In this case x can equal 2 or -2, so this equation has two solutions. An example of an equation with an infinite number of solutions is x + 6 = 3*2 + x. x can equal any number to make this equation true, so it has an infinite number of solutions. The equation x = x + 1 is an example of an equation with no solutions.)
What are two equations that have the same solution?
equal equations.
What is the solution to the system of these equations Y equals 2X and Y -X 3 is?
-1
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 :)
Why do quadratic equations where the discriminant is 0 have exactly 1 real solution?
Suppose the quadratic equation is ax^2 + bx + c = 0 and D = b^2 - 4ac is the discriminant. Then the solutions to the quadratic equation are [-b ± sqrt(d)]/(2a). Since D = 0, the both solutions are equal to -b/(2a), a single real solution.
What is algebraic strategy for solving a system of equations when two expressions are the same?
An expression is the algebraic representation of a number - an expression has a numeric value.An equation is an algebraic statement claiming that two expressions have the same numeric value. The equation has a Boolean value (true or false).If two equations can be expressed in an identical manner (the same expression on both sides) - then these equations are the same equation.In order for a system of equations to have a solution, the number of different equations in the system must be equal to the number of variables in the system. If there are more distinct equations than there are variables, than the system has no solution. If there are less, then the system may have no solution, or infinitely many solutions.In the case described there is most likely an infinite number of solutions
What is the answer called in a equation?
The answer in an equation is called the "solution." It is the value or values that satisfy the equation, making both sides equal when substituted into the expression. In the case of equations with multiple variables, the solution may represent a set of values.
How do you solve a system of equations approximately using graphs and tables?
To solve a system of equations approximately using graphs and tables, you can start by graphing each equation on the same coordinate plane. The point where the graphs intersect represents the approximate solution to the system. Alternatively, you can create a table of values for each equation, identifying corresponding outputs for a range of inputs, and then look for common values that indicate where the equations are equal. This visual and numerical approach helps to estimate the solution without exact calculations.
When can two equations be equal?
Two equations are equal when the result of the functions of the numbers and variables of one equation match the results of the other equation.
Why is it important to keep both sides of the equation equal?
If both sides of an equation are not equal, it won't be an equation any more! In solving equations, the strategy is to change both sides in the same way, so that an 'equivalent' equation is produced. An equivalent equation has the same solution as the original equation. You are aiming for an equation in which the variable is alone on one side. The quantity on the other side is the solution.
What does one solution mean in math?
An equation may have zero, one, or more solutions (this is also true for a system of equations). The equation 2 + x = 5 has only solution, for example. x can only equal 3, so there is one solution. (An example of an equation with more that one solution is x2 = 4. In this case x can equal 2 or -2, so this equation has two solutions. An example of an equation with an infinite number of solutions is x + 6 = 3*2 + x. x can equal any number to make this equation true, so it has an infinite number of solutions. The equation x = x + 1 is an example of an equation with no solutions.)
What are two equations that have the same solution?
equal equations.
What is the solution of the system of linear equations x equals 0 and y equals 0?
The solution of the system of linear equations ( x = 0 ) and ( y = 0 ) is the single point (0, 0) in the Cartesian coordinate system. This point represents the intersection of the two equations, where both variables are equal to zero. Thus, the only solution is the origin.
What happens if you are checking a solution for the radical expression and find that it makes one of the denominators in the expression equal to zero?
Then it is not a solution of the original equation. It is quite common, when solving equations involving radicals, or even when solving equations with fractions, that "extraneous" solutions are added in the converted equation - additional solutions that are not solutions of the original equation. For example, when you multiply both sides of an equation by a factor (x-1), this is valid EXCEPT for the case that x = 1. Therefore, in this example, if x = 1 is a solution of the transformed equation, it may not be a solution to the original equation.
How are equations and expressions different?
An expession has NO equal sign, a equation are to amounts that are equal
How are equations different from inequalities?
Equations are statements that state two expressions are equal, while inequalities are statements that state two expressions are not equal, meaning one is greater or less than the other. The graph of the solution set of an equation is a line or a curve, while the graph of the solution set of an inequality is a region at one side of the boundary line or curve obtained by supposing that the inequality was an equation.
What is consistent and dependent?
The terms consistent and dependent are two ways to describe a system of linear equations. A system of linear equations is dependent if you can algebraically derive one of the equations from one or more of the other equations. A system of linear equations is consistent if they have a common solution.An example of a dependent system of linear equations:2x + 4y = 84x + 8y = 16Solve the first equation for x:x = 4 - 2yPlug that value of x into the second equation:16 - 8y + 8y = 16, which gives 16 = 16.No new information was gained from the second equation, because we already knew 16 = 16, so these two equations are dependent.An example of an inconsistent system of linear equations:Because consistency is boring.2x + 4y = 84x + 8y = 15Solve the first equation for x:x = 4 - 2yPlug that value of x into the second equation:16 - 8y + 8y = 15, which gives 16 = 15.This is a contradiction, because 16 doesn't equal 15. Therefore this system has no solution and is inconsistent.
