Solving simultaneous equations

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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