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Title: Simultaneous Equation
Description: Simultaneous equations are a set of equations that contain multiple variables and are solved simultaneously. These types of equations are used to model real-world situations where more than one unknown is present. we will explore each of these methods in more details and learn how to apply them to solve simultaneous equations. We will also discuss the use of matrices and determinants in solving simultaneous equations and introduce the concept of systems of linear equations. By the end of this guide, you should have a solid understanding of simultaneous equations and be able to confidently solve them using a variety of methods.
Description: Simultaneous equations are a set of equations that contain multiple variables and are solved simultaneously. These types of equations are used to model real-world situations where more than one unknown is present. we will explore each of these methods in more details and learn how to apply them to solve simultaneous equations. We will also discuss the use of matrices and determinants in solving simultaneous equations and introduce the concept of systems of linear equations. By the end of this guide, you should have a solid understanding of simultaneous equations and be able to confidently solve them using a variety of methods.
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bracket the solution (i
...
the solution lies between them)
...
The process is repeated until the solution is found to the desired
level of accuracy
...
Example 1:
Solve the system of equations x^2 + y^2 = 4 and xy = 1
...
Step 2: Evaluate the function at the midpoint of the interval
...
At the point (1, 1), the function values are [-3, 0]
...
If both function values have the same sign, then the root must lie in one of
the subintervals formed by dividing the original interval in half
...
Step 4: Repeat steps 2 and 3 until the interval is small enough to be considered the
approximate solution
...
Therefore, the solution to the system of equations is x = 1 and y = 1, with an error of +/- 0
...
Example 2:
Solve the system of equations x^2 + y^2 = 4 and x + y = 2
...
Step 2: Evaluate the function at the midpoint of the interval
...
At the point (0, 0), the function values are [-4, 0]
...
If both function values have the same sign, then the root must lie in one of
the subintervals formed by dividing the original interval in half
...
Step 4: Repeat steps 2 and 3 until the interval is small enough to be considered the
approximate solution
...
Therefore, the solution to the system of equations is x = 0 and y = 0, with an error of +/- 1
...
Infinite solutions
In some cases, it is possible for a system of simultaneous equations to have an infinite number
of solutions
...
For example, the system of equations x + y =
4 and 2x + 2y = 8 has an infinite number of solutions, because the second equation is simply
the first equation multiplied by 2
...
This
occurs when the equations are contradictory, meaning that there is no set of values that can
satisfy both equations simultaneously
...
Nonlinear equations
Simultaneous equations can also be nonlinear, meaning that they contain terms that are not a
linear combination of the variables
Title: Simultaneous Equation
Description: Simultaneous equations are a set of equations that contain multiple variables and are solved simultaneously. These types of equations are used to model real-world situations where more than one unknown is present. we will explore each of these methods in more details and learn how to apply them to solve simultaneous equations. We will also discuss the use of matrices and determinants in solving simultaneous equations and introduce the concept of systems of linear equations. By the end of this guide, you should have a solid understanding of simultaneous equations and be able to confidently solve them using a variety of methods.
Description: Simultaneous equations are a set of equations that contain multiple variables and are solved simultaneously. These types of equations are used to model real-world situations where more than one unknown is present. we will explore each of these methods in more details and learn how to apply them to solve simultaneous equations. We will also discuss the use of matrices and determinants in solving simultaneous equations and introduce the concept of systems of linear equations. By the end of this guide, you should have a solid understanding of simultaneous equations and be able to confidently solve them using a variety of methods.