Substitution Method for Solving Pair of Linear Equations

Substitution Method for solving Pair of Linear Equations. Substitution Method for solving pair of linear equations involves following steps: 1. Simplify the equations given to get coefficients which can be manipulated . Select and solve one of the equations i.e write one variable in terms of other variable !. Substitute the variable in other equation ". Solve the equation with one variable #. $se the value of variable in other equation and solve the equation %. &rite the solution Example for Substitution Method: Method:  Solve the following pair of linear equations using substitution method. '(" ) y

*"

'( ) y(! * ! Step 1: 1: Simplify the Equations.

' ) "y * 1% !' ) y * 1+

,-ae L/M and mae /oefficients as natural

numbers0 Step 2: 2: &rite one variable in terms of other ' * 1%  "y  -he coefficient of ' in first equation is 1. So it is easy to write ' in terms of y. Step 3: 3: Substitute the variable in other equation !,1%  "y0 ) y * 1+

Step 4: 4: Solve the equation with one variable. !,1%  "y0 ) y * 1+ *2 "+  1y ) y * 1+ or 13y * !3 or y *!

Step 5: $se the value of variable ,y0 in one of the equations to solve for other variable '(" ) ! * " *2 '(" * 1 *2 ' * " Step 6: -he solution is given by ' * " and y * ! 4f you find it difficult to understand the steps by yourself5 please have a loo at following videos.

 &hen should the substitution method be used for solving pair of linear equations6 1. &hen the coefficients of one or more of the variables are 1. . &hen the coefficients of variables are can be reduced to 1. !. 4f denominators of fractions have small natural numbers as L/M. ". -here are no decimals involved. Elimination Method for solving pair of linear equations. -his page gives general method of solving pair of linear equations using elimination method. 7or special cases such as those with unique solution5 infinite solutions and no solution5 please refer to page on special cases. Elimination method for solving pair of linear equations involves following steps: 1. /hec for the coefficients of variables in given equations and simplify the equations. . 4f any two variables have same coefficients5 subtract one equation from the other. !. 8therwise5 mae coefficients of a variable equal in two equations by multiplying with different numbers. ". Subtract one equation from the other. #. Solve for the variable from simple equation. %. $se the value of this variable to solve for other variable. 9. &rite the Solution E'ample for Elimination Method:

Solve the following pair of linear equations using elimination method. '(" ) y

* "  ,10

'( ) y(! * !  ,0 Step 1: /hec for the coefficients and Simplify the Equations. ' ) "y * 1%  ,!0 !' ) y * 1+  ,"0

,-ae L/M and mae /oefficients as natural numbers0

Step 2: 4f any two variables have same coefficients5 subtract one equation from the other. 4n the given equations5 no two variables have same coefficients. So5 we need to mae the coefficients equal. Step 3: 8therwise5 mae coefficients of a variable equal in two equations by multiplying with different numbers. Equation ,!0 can be multiplied by ! to mae coefficients of ' equal. Equation ,"0 can be multiplied by  to mae coefficients of y equal.  &e will solve by multiplying equation ,!0 with !. !' ) 1y * "+ ,#0 !' ) y * 1+ ,"0 Step 4: Subtract on equation from other. Step 5: Solve for the variable from simple equation. ,#0  ,"0 gives 13y * !3 *2 y * ! Step 6: $se the value of this variable to solve for other variable. Putting value of y in equation ,"05 we have !' ) % * 1+ *2 !' * 1 *2 ' * " Step 7: -he solution is given by ' * " and y * ! 4f you find it difficult to understand the steps by yourself5 please have a loo at the following videos.

youtube*http:((www.youtube.com(watch6v*iEdyoP3En!c;  hen should elimination method be used for solving pair of linear equations! 1. &hen coefficient of one variable are equal in b oth equations . &hen L/M of coefficients of same variable is small number !. Multiplication to mae coefficients does not result in large numbers ". Less calculation involving decimals and fractions "raphi#al Method for Solving $air of %inear Equations:
=ewrite the given equations in form of standard line equation y * m' ) c

. >erify if the slopes ,m0 are equal in two equations !.

4f slopes are equal5 then chec if the constants are equal

". 4f slopes are equal and constants are not equal5 conclude that the lines are parallel #.

4f both the slopes and constants are equal5 they represent same line

%. 4f slopes are not equal in standard form5 plot the graphs of two equations 9.

-he point of intersection gives the solution for pair of linear equations

E'ample for erify if the slopes,m0 are equal in two equations

 &e see the slope of equation ,!0 is 1 and slope of equation ,"0 is 1 Step !: 4f slopes are equal5 then chec if the constants are equal -he slopes are not equal as seen in step . /onstants are also not equal. Step ": 4f slopes are equal and constants are not equal5 conclude that the lines are parallel Step #: 4f both the slopes and constants are equal5 they represent same line  @s both the slopes and constants are not equal5 the given lines are different and are not parallel. Step %: 4f slopes are not equal in standard form5 plot the graphs of two equations Step 9: -he point of intersection is given by ' * ! and y * 1