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Procedure - Solving simultaneous equations, Math, Class 9 | Extra Documents & Tests for Class 9 PDF Download

LCM Method:

1. Select a variable to eliminate by using LCM method.
2. Calculate the LCM of coefficients of the variable to eliminate, from both the equations.
3. Multiply both the equations by 'LCM divided by coefficient of the variable to eliminate'.
4. Simplify the equations.
5. Subtract one equation from the another to get one equation in one variable.
6. Divide RHS by coefficient of the variable to get value of one variable.
7. Substitute this value in any of the two equations to get one equation in one variable.
8. Simplify the equation and divide the RHS by the coefficient of the variable to get value of the other variable.

Substitution Method:

1. Select a variable to eliminate by using substitution method.
2. Select the way of substitution i. e. you want to substitute value of variable from equation (1) into equation (2) or from equation (2) into equation (1).
3. Find an expression for the selected variable.
4. Substitute this expression in place of the variable in other equation. (For example, if you have derived expression from equation (1), then substitute this expression in equation (2) and vice versa)
5. Simplify this equation and collect the like terms together such that you will get one equation in one variable.
6. Divide RHS by the coefficient of the variable in order to get value of one variable.
7. Substitute this value in any of the two equations to get one equation in one variable.
8. Simplify the equation and divide the RHS by the coefficient of the variable to get value of the other variable.

Observations:
Number of variables in a linear equation is equal to the number of equations required to find the values of the variables.

Result:
Linear Simultaneous Equations are successfully solved by using any of the two methods which are LCM method and Substitution method.

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FAQs on Procedure - Solving simultaneous equations, Math, Class 9 - Extra Documents & Tests for Class 9

1. What are simultaneous equations?
Ans. Simultaneous equations are a set of equations that are solved together to find the values of the variables that satisfy all the equations at the same time. In other words, these equations are solved simultaneously to find the common solutions.
2. How can I solve simultaneous equations?
Ans. There are different methods to solve simultaneous equations, such as the substitution method, elimination method, and graphical method. In the substitution method, we solve one equation for one variable and substitute it into the other equation. In the elimination method, we manipulate the equations to eliminate one variable and solve for the other. The graphical method involves plotting the equations on a graph and finding the intersection point as the solution.
3. Can simultaneous equations have no solution?
Ans. Yes, simultaneous equations can have no solution. This happens when the equations represent parallel lines that never intersect. In such cases, the values of the variables cannot satisfy both equations simultaneously, resulting in no common solution.
4. Is it possible to have infinite solutions for simultaneous equations?
Ans. Yes, it is possible to have infinite solutions for simultaneous equations. This occurs when the equations represent the same line or are multiples of each other. In such cases, every point on the line(s) is a solution, resulting in an infinite number of solutions.
5. Are there any real-life applications of simultaneous equations?
Ans. Yes, simultaneous equations have various real-life applications. They can be used to solve problems related to finance, physics, engineering, and many other fields. For example, they can be used to determine the optimal production levels in a manufacturing company, analyze the interaction between multiple forces in a physics problem, or find the intersection point of two moving objects.
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