Solve the following system of equations by the elimination method and the substitution method:
Elimination method
Step(1): Making coefficient of variableequal
Multiply the given equation needed by a suitable number so that the coefficient of one of the variables says become equal.
Multiply by in and multiply by in which make coefficient equal.
Step (2): Eliminating the variable
Subtract the equations obtained in step- to eliminate one variable. The resulting equation is a linear equation in one variable..
Step (3): Obtain value of other variable
Substitute this value of the variable in either of the original equations, to get the value of the other variable.
multiplying the equation throughout by
Hence
Substitution Method
Step(1):Express one variable in terms of other
Express one variable in terms of other variable from one of the given equations.
Step (2): Use the second equation
Substitute this value of x in the other equations to get a linear equations in which can be solved.
multiplying the equation throughout by 2
Step (3) : Finding the other variable.
Substitute the values of obtained in step- above in the equations used in step- to get the values of .
Hence,by both mehod answer is same and