Dear Suresh

Solving systems of equations graphically is one of the easiest ways to solve systems of simple equations

Another way to solve systems of equations is by substitution.  In this method, you solve on equation for one variable, then you substitute that solution in the other equation, and solve.  Example:

1. Problem: Solve the following system:
            x + y = 11
            3x - y = 5
            
  Solution: Solve the first equation for y
            (you could solve for x - it
            doesn't matter).
            
            y = 11 - x
            
            Now, substitute 11 - x for y
            in the second equation. This gives
            the equation one variable, which
            earlier algebra work has taught
            you how to do.
            
            3x - (11 - x) = 5
            3x - 11 + x = 5
            4x = 16
            x = 4
            
            Now, substitute 4 for x in
            either equation and solve for y.
            (We use the first equation below.)
            
            4 + y = 11
            y = 7

Solve the following system:
             x + y + z  = 4
             x - 2y - z = 1
            2x - y - 2z = -1

  Solution: Start out by multiplying the
            first equation by -1 and add
            it to the second equation to 
            eliminate x from the second
            equation.

            -x  - y - z = -4
             x - 2y - z = 1
            ----------------
               -3y - 2z = -3

            Now eliminate x from the third
            equation by multiplying the first
            equation by -2 and add it to
            the third equation.

            -2x - 2y - 2z = -8
             2x -  y - 2z = -1
            ------------------
                 -3y - 4z = -9

            Next, eliminate y from the third
            equation by multiplying the second
            equation by -1 and adding it to
            the third equation.

             3y +  2z = 3 
            -3y -  4z = -9
            --------------
                  -2z = -6

            Solve the third equation for z.
                 
            -2z = -6
              z = 3

            Substitute 3 for z in the
            second equation and solve for y.

            -3y - 2z = -3
            -3y - 2(3) = -3
            -3y - 6 = -3
            -3y = 3
            y = -1

            Lastly, substitute -1 for y and
            3 for z in the first equation
            and solve for x.

            x + (-1) + 3 = 4
            x + 2 = 4
            x = 2

All the best.
AKASH GOYAL
AskiitiansExpert-IITD
 
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