Yes, radical equations can sometimes have extraneous solutions. When solving these equations, squaring both sides to eliminate the radical can introduce solutions that do not satisfy the original equation. Therefore, it is essential to check all potential solutions in the original equation to verify their validity.
There are several good websites to find help with radical equations. You tube has several good videos on radical equations that are free of charge.
The answers to equations are their solutions
If a system of equations is inconsistent, there are no solutions.
radical equations have sq roots, cube roots etc. Quadratic equations have x2.
Yes, radical equations can sometimes have extraneous solutions. When solving these equations, squaring both sides to eliminate the radical can introduce solutions that do not satisfy the original equation. Therefore, it is essential to check all potential solutions in the original equation to verify their validity.
There are several good websites to find help with radical equations. You tube has several good videos on radical equations that are free of charge.
Simultaneous equations have the same solutions.
The answers to equations are their solutions
If a system of equations is inconsistent, there are no solutions.
Equations do have solutions, sometimes they may be a little difficult to figure out.
radical equations have sq roots, cube roots etc. Quadratic equations have x2.
Simultaneous equations have the same solutions
The basic method is the same as for other types of equations: you need to isolate the variable ("x", or whatever variable you need to solve for). In the case of radical equations, it often helps to square both sides of the equation, to get rid of the radical. You may need to rearrange the equation before squaring. It is important to note that when you do this (square both sides), the new equation may have solutions which are NOT part of the original equation. Such solutions are known as "extraneous" solutions. Here is a simple example (without radicals): x = 5 (has one solution, namely, 5) Squaring both sides: x squared = 25 (has two solutions, namely 5, and -5). To protect against this situation, make sure you check each "solution" of the modified equation against the original equation, and reject the solutions that don't satisfy it.
To determine the number of solutions for a system of equations, one would typically analyze the equations' characteristics—such as their slopes and intercepts in the case of linear equations. If the equations represent parallel lines, there would be no solutions; if they intersect at a single point, there is one solution; and if they are identical, there would be infinitely many solutions. Without specific equations, it's impossible to provide a definitive number of solutions.
You need to check for extraneous solutions when solving equations containing variables in denominators or within radical expressions. These solutions may arise from introducing new roots or excluded values during manipulations, which need to be verified to ensure they are valid in the original equation.
As there is no system of equations shown, there are zero solutions.